х + Х Student MasteryConnect :: Home Clever Portal Tip https://student.masteryconnect.com/?iv=Q9PrkhJCb4100tK|4bkYtw&tok=dg Qa1GEHKDXUKGzkK_Vc7W... 6-8 Approved Sites POS *commoncore equa... Fin 7 8 9. 11 14 5 10 12 13 6 10 of 18 SCS_20-21_Math_GRZ_CFA2 Davis, Tra'mon The cost before tax for an order of CDs from Music & More store was $214.60. If the store ordered 20 equally priced CDs, and the total shipping and handling fee was $15.00, what was the cost of one CD? $9.98 $10.73 $11.48 $14.31
Answers
199.60/20= 9.98
Each cd was $9.98
Related Questions
Evaluate this expression.
8x, if x = 6
Answers
Answer:
48
Step-by-step explanation:
8 times 6 = 48
Answer:
\( \huge{ \fbox{ \sf{48}}}\)
Step-by-step explanation:
\( \underline{ \sf{Given}} = \sf{x = 6}\)
\( \underline{ \sf{To \: Find}} : \sf{Value \: of \: the \: given \: expression} \)
\( \sf{8x}\)
plug the value of x
\( \mapsto{ \sf{8 \times 6}}\)
Multiply the numbers
\( \mapsto{ \sf{48}}\)
Hope I helped!
Best regards! :D
~\( \text{TheAnimeGirl}\)
17 Answer:
Decide how many solutions this equation has:
x2 - 2x + 1 = 0
18 Answer:
Decide how many solutions this equation has:
x2 + 3 = 0
19 Answer:
The revenue from selling x units of a product is given by
y = -0.0002x2 + 20x. How many units must be sold in
order to have the greatest revenue? (Find the x-coordinate
of the vertex of the parabola.)
Answers
ASAP, PLSSS!!!! What is the range of the given function?
Answers
Answer:
[6, 8).
Step-by-step explanation:
When we are looking for the range of a function by just looking at the graph, we have to define from what point to what point the graph move vertically. On the other hand, if we were looking for the domain, we would state from where to where the graph moves horizontally.
In this case we have to analyze the graph vertically, since we are looking for the range of the function. Therefore, if we take a look at the line we can notice that it goes from y=6 to y=8. Therefore the range should be from 6 to 8.
Now, this result must be expressed in interval notation, meaning that we have to state whether the values of each end are contained or not by the function. The graph already tells us about it., because it marks it with the closed or open dots. In the case of the number 6, we have a closed dot, means that the function contains the number 6. For the other end we have an open dot, means that the function doesn't contain the number 8.
Applying internal notation, the range of this function is:
[6, 8).
Learn more about interval notation here:
1. https://web.nmsu.edu/~kberver/Unit1/Unit18.html#:~:text=An%20interval%20is%20closed%20if,used%20for%20an%20open%20endpoint.
2. https://brilliant.org/wiki/interval-notation/#:~:text=Interval%20notation%20is%20a%20way,inequality%20or%20system%20of%20inequalities.
I need help with this differential equation.
Answers
(i) The partial fraction decomposition of\(100/(x^7 * (10 - x))\) is\(100/(x^7 * (10 - x)) = 10/x^7 + (1/10^5)/(10 - x).\) (ii) The expression for t in terms of x is t = 10 ± √(100 + 200/x).
(i) To express the rational function 100/(\(x^7\) * (10 - x)) in partial fractions, we need to decompose it into simpler fractions. The general form of partial fractions for a rational function with distinct linear factors in the denominator is:
A/(factor 1) + B/(factor 2) + C/(factor 3) + ...
In this case, we have two factors: \(x^7\) and (10 - x). Therefore, we can express the given rational function as:
100/(\(x^7\) * (10 - x)) = A/\(x^7\) + B/(10 - x)
To determine the values of A and B, we need to find a common denominator for the right-hand side and combine the fractions:
100/(x^7 * (10 - x)) = (A * (10 - x) + B * \(x^7\))/(\(x^7\) * (10 - x))
Now, we can equate the numerators:
100 = (A * (10 - x) + B * \(x^7\))
To solve for A and B, we can substitute appropriate values of x. Let's choose x = 0 and x = 10:
For x = 0:
100 = (A * (10 - 0) + B * \(0^7\))
100 = 10A
A = 10
For x = 10:
100 = (A * (10 - 10) + B *\(10^7\))
100 = B * 10^7
B = 100 / 10^7
B = 1/10^5
Therefore, the partial fraction decomposition of 100/(\(x^7\) * (10 - x)) is:
100/(\(x^7\) * (10 - x)) = 10/\(x^7\) + (1/10^5)/(10 - x)
(ii) Given the differential equation: dx/dt = (1/100) *\(x^2\) * (10 - x)
We are also given x = 1 when t = 0.
To solve this equation and obtain an expression for t in terms of x, we can separate the variables and integrate both sides:
∫(1/\(x^2\)) dx = ∫((1/100) * (10 - x)) dt
Integrating both sides:
-1/x = (1/100) * (10t - (1/2)\(t^2\)) + C
Where C is the constant of integration.
Now, we can substitute the initial condition x = 1 and t = 0 into the equation to find the value of C:
-1/1 = (1/100) * (10*0 - (1/2)*\(0^2\)) + C
-1 = 0 + C
C = -1
Plugging in the value of C, we have:
-1/x = (1/100) * (10t - (1/2)\(t^2\)) - 1
To solve for t in terms of x, we can rearrange the equation:
1/x = -(1/100) * (10t - (1/2)\(t^2\)) + 1
Multiplying both sides by -1, we get:
-1/x = (1/100) * (10t - (1/2)\(t^2\)) - 1
Simplifying further:
1/x = -(1/100) * (10t - (1/2)\(t^2\)) + 1
Now, we can isolate t on one side of the equation:
(1/100) * (10t - (1/2)t^2) = 1 - 1/x
10t - (1/2)t^2 = 100 - 100/x
Simplifying the equation:
(1/2)\(t^2\) - 10t + (100 - 100/x) = 0
At this point, we have a quadratic equation in terms of t. To solve for t, we can use the quadratic formula:
t = (-(-10) ± √((-10)^2 - 4*(1/2)(100 - 100/x))) / (2(1/2))
Simplifying further:
t = (10 ± √(100 + 200/x)) / 1
t = 10 ± √(100 + 200/x)
Therefore, the expression for t in terms of x is t = 10 ± √(100 + 200/x).
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how do you find the remaining side of a 45°-45°-90° triangle if the longest side is 28?
Answers
Here you go! Hope this helps
A bike path is 12.5 miles. Dominic is 70% of the way to the end. How far is Dominic on the path?
Answers
The percentage of the distance Dominic is on the path is his distance
travelled as a fraction of the total distance when equivalent to 100.
The distance he has travelled on the path is 8.75 miles.
The given parameter are;
Length of Dominic's path = 12.5 miles
The length of the way Dominic is to the end = 70%
Required:
The distance Dominic has travelled on the path
The distance Dominic has travelled, D is 70% of 12.5 miles.
70% of 12.5 miles = 70% × 12.5 miles = 8.75 miles
The distance Dominic has travelled on the path, D = 8.75 miles
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Find a solution to the linear equation 14x−y=−14 by filling in the boxes with a valid value of x and y.
Answers
Answer:
28x=y
Step-by-step explanation:
28x=y because 14x-y=-14 plus y on both sides=
14x=-14y then add 14 to both sides=
28x=y
The values of x and y that will make the equation correct are:
x = 1 and y = 28
How to find a solution to the Linear Equation?The linear equation is given as:
14x - y = -14
Now, we want to find the values of x and y for which the equation is correct. Thus:
we can choose a value for x and then solve for y, or we can choose a value for y and then solve for x. Let's choose a value for x and solve for y:
Let x = 1
Substitute 1 for x to get:
14(1) - y = -14
14 - y = -14
14 + 14 = y
y = 28
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suppose you roll two six-sided dice. let the macrostate s of the two dice be the sum of their top faces.
Answers
The macrostate s of two six-sided dice can be defined as the sum of the top faces of the dice.
The macrostate of a system refers to a comprehensive description of the system in terms of its properties and variables that are used to characterize it. In the case of two six-sided dice, the macrostate is described by the sum of the numbers on the top faces of the two dice, which determines the total score or outcome. This macrostate, represented by the variable "s", is a measurable quantity that summarizes the state of the system, providing information about the distribution of the outcomes over all possible configurations of the two dice.
It's important to note that a macrostate does not specify the exact configuration of the system, but rather provides a probabilistic description of it. In other words, the macrostate "s" only describes the sum of the two dice and does not specify which number is on each die. In thermodynamics, macrostates are used to characterize the thermodynamic properties of a system, such as its temperature, pressure, and entropy. The study of macrostates and their distributions helps us to understand the behavior of complex systems and make predictions about their future behavior.
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Help me with this please :V
Answers
Answer:
refer to the above attachment
A man is 13 times as old as his son is. In 10 years he will be 3 times as old as his son is now. How old are they now?
Answers
Answer:
the son is 2
man is 26
+10 yrs
son=12
man=36
Step-by-step explanation:
Let the son's age be x.
Then the father's age is 13x.
In ten years their ages will be (x+10) and (13x+10).
(13x+10)=3(x+10)
13x+10=3x+30
10x=20
x=2
The son is 2 years old.
simplify 18x8/6/4x
HELP
Answers
Answer:
6/x.
Step-by-step explanation:
18x8/6/4x
= 144/6/4x
= 24/4x
= 6/x.
Students at Sunnyvale Middle School volunteered to work a 2-hour shift at a
car wash fundraiser. The table shows the number of people who worked each
shift and how many cars they washed.
Is the relationship between the number of
cars washed and the number of workers
proportional? Complete the statement.
The number of cars washed per person
?
of workers, so the relationship is
the same for each number
?
People Working
4
6
8
10
Cars Washed
8
12
20
25
Answers
The relationship in this problem is not proportional, as there are different ratios between the number of people and the number of cars washed.
What is a proportional relationship?A proportional relationship is a relationship in which a constant ratio between the output variable and the input variable is present.
The equation that defines the proportional relationship is a linear function with slope k and intercept zero given as follows:
y = kx.
The slope k is the constant of proportionality, representing the increase or decrease in the output variable y when the constant variable x is increased by one.
The ratios between the output and the inputs are given as follows:
8/4 = 2.12/6 = 2.20/8 = 2.5.25/10 = 2.5.Different ratios, hence the relationship is not proportional.
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if the letter l,o,g,ic are randomnly arranged to form word logic what is the probability that result will be woord logic
Answers
The probability of randomly forming the word "woord logic" is:Probability = 1 / (10! / (2!))
To calculate the probability of forming the word "woord logic" by randomly arranging the letters l, o, g, i, c, we need to consider the total number of possible arrangements and the number of arrangements that result in the desired word.
The word "woord logic" has 10 letters in total. Among these letters, there are 2 o's and the remaining letters appear only once.
The total number of possible arrangements is given by the factorial of the total number of letters:
Total arrangements = 10!
However, since the letter "o" appears twice, we need to divide by the factorial of the number of repeated letters:
Total arrangements = 10! / (2!)
To calculate the number of arrangements that result in "woord logic," we consider that the arrangement of "woord logic" is unique and distinct. Thus, there is only one arrangement that matches the desired word.Simplifying this expression would yield the exact probability.
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Which shows the pre-image of triangle XYZ' before the figure was rotated 90° about the origin?
Answers
Answer: 2nd picture
Step-by-step explanation: its rotating 90 degrees
I need help it’s due in 20 min:(
Answers
Answer:
A) DF= 11
B) JH= 13.6
C) GJ= 23.6
D) m∠F= 105
E) m∠G= 34
F) m∠J= 41
Step-by-step explanation:
A farmer wants to increase the area of his rectangular pen but keep the pen a rectangular shape He decides to add 1.3 meters of
fencing to the width of the pen but the length will remain 10.4 meters. The new area will be 81.12 square meters
Which equation can be used to determine the original width, w of the pen?
Answers
Answer:
81.12 square meters
Step-by-step explanation:
Using the equation for the area of a rectangle, the original width w of the pen is determined by 10.4(w + 1.3) = 81.12
What is the area of the rectangle?The area of the rectangle is the product of the length and width of a given rectangle.
The area of the rectangle = length × Width
Given that farmer wants to increase the area of his rectangular pen but keep the pen a rectangular shape then he decides to add 1.3 meters of
fencing to the width of the pen but the length will remain 10.4 meters.
Length = 10.4 meters.
Width w = (w + 1.3)
The new area of rectangle = 81.12 square meters
Then: Using the equation for the area of a rectangle, the original width w of the pen is determined by 10.4(w + 1.3) = 81.12
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2
One type of redwood tree has an average height of 65 feet when it is 20 years old. If the tree is more than 20 years
old, the average height, h, can be modeled by the function h = 1.95(a - 20) + 65, where a is the age of the tree in
years. Which statement about this situation is true?
A Every additional 1.95 ft of length over 20 ft adds 45 years to the age of this type of redwood tree.
8. For this type of redwood tree, the average height increases by 1.95 ft per year throughout its lifetime.
c. Each additional year of age over 20 years adds 1.95 ft to the average height of this type of redwood tree.
D. For this type of redwood tree, the average height increases by 65 ft for every 20 years of growth.
Answers
Each additional year of
What is the value of x?
P
80°
x+84°
3x
R
Q
Answers
Answer:
x = 49
Step-by-step explanation:
The sum of angles is 360
(x + 84) + 80 + 3x = 360
x + 3x = 360 - 84 - 80
4x = 196
x = 196/4 = 49
Which of the following rational functions is graphed below
Answers
Answer:
A.
Step-by-step explanation:
if x≠-4, then the correct answer is
\(A. \ F(x)=\frac{1}{x+4}.\)
How many calories in the candy bars
Answers
Answer:
A = 267 calories; B = 257 calories
Step-by-step explanation:
We can set up a system of equations to find how many calories each candy bar provides.
The information gives us:
A + 2B = 781 and 2A + B = 791.
Substitution will be easier, and we can isolate A from the first equation and then plug it in for A in the second equation:
\(A+2B=781\\2A+B=791\\\\A=781-2B\\\\2(781-2B)+B=791\\1562-4B+B=791\\1562-3B=791\\-3B=-771\\B=257\)
Now we can plug in B into the first equation to find A:
\(A+2(257)=781\\A+514=781\\A=267\)
100 POINTS!!! A group of students were asked if they carry a credit card. The responses are listed in the table. If a student is selected at random, find the probability that he or she owns a credit card given that the student is a freshman. Round your answer to three decimal places.
Answers
Since it’s saying their is a student selected at random that means it is out of 100 students. Then it’s asking for freshman who have a credit card which is 21 people. That means it’s 21/100 which is .21 probability.
Answer:
0.350 (3 d.p.)
Step-by-step explanation:
\(\sf Probability\:of\:an\:event\:occurring = \dfrac{Number\:of\:ways\:it\:can\:occur}{Total\:number\:of\:possible\:outcomes}\)
Let P(A) = probability that the student is a freshman
Let P(B) = probability that the student owns a credit card
Use the given table to calculate the probability that the student is a freshman:
\(\implies \sf P(A)=\dfrac{60}{100}=0.6\)
And the probability that the student is a freshman and owns a credit card:
\(\implies \sf P(A \cap B)=\dfrac{21}{100}=0.21\)
To find the probability that the student owns a credit card given that the they are a freshman, use the conditional probability formula:
Conditional Probability Formula
The probability of B given A is:
\(\sf P(B|A)=\dfrac{P(A \cap B)}{P(A)}\)
Substitute the found values into the formula:
\(\implies \sf P(B|A)=\dfrac{0.21}{0.6}=0.35\)
Therefore, the probability that the student owns a credit card given that they are a freshman is 0.35
In the equation y = 39x + 50represents the number of people at a holiday dinner and y represents the total cost of
the dinner. If a family spent $518, how many people attended the dinner?
Answers
Answer:
The correct answer is - 12.
Step-by-step explanation:
Given:
Total number of people = y = 39x+50
Total amount spent y = 518
Solution:
The equation for the number of people who attended the dinner
y = 39x+50
The cost of dinner is equally divided by number of people =
then, 518 = y
placing value, 518 = 39x+50
x = (518-50)/39
= 468/39
= 12
Then number of people attended the dinner = 12
IN CASE YOU ARE LOOKING FOR THE ANSWER
A climber is standing at the top of Mount Kilimanjaro, approximately 3.7 mi above sea level. Earth has a radius of 3959 mi.
What is the climber's distance to the horizon?
Enter your answer as a decimal in the box. Round only your final answer to the nearest tenth.
Answers
Answer: The answer is 171.2 Miles
Step-by-step explanation: You can easily find a "Horizon finder" online. It helps for harder equations like this.
Also I just realized that you put 171.20. When a question asks for a nearest tenth, only put the first digit of the decimal.
A factory that makes statues is trying to maximize its income. Their two primary products are the Liberty and David statues. Each Liberty requires 18 minutes of machine time to rough cut the shape and 36 minutes of artist time to finish the details. The David requires 27 minutes on the machines and 18 minutes with the artist's hand. The factory is limited each day to 162 minutes of machine time and 216 minutes of artist time. Both use 7 pounds of stone, and the factory has 49 pounds of stone available per day. If each Liberty brings in a profit of sixty-three dollars, and each David brings in ninety-six dollars, how many statues of each type should the factory make each day?
Constraints:
⎧
⎪
⎨
⎪
⎩
18
L
+
27
D
≤
162
36
L
+
18
D
≤
216
7
L
+
7
D
≤
49
Objective:
Income =
63
L
+
96
D
Answers
Optimizing function describes the minimum or maximum output from the function.
The factory should make 3 David statues and 4.5 Liberty statues
The constraints and the objective function are given as:
\(\mathbf{18L + 27 D \le 162}\)
\(\mathbf{36L + 18 D\le 216}\)
\(\mathbf{7L + 7D \le 49}\)
\(\mathbf{Objective:\ Income = 63L+ 96D}\)
We start by plotting the graphs of the inequalities, where L is represented on the vertical axis, and D on the horizontal axis
From the graph, the only optimal point is: D = 3 and L = 4.5
Hence, the factory should make 3 David statues and 4.5 Liberty statues
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Exponential Data
In this activity, you will graph and write exponential functions to model population data presented in tables. Then you’ll use your models to make predictions and draw a conclusion.
Question 1
A town’s population has been exponentially increasing for the past 10 years. The town council initially recorded the town’s population at 6,000 people and tracked it each year after that. The table represents their data.
Years Town Population
(in thousands)
0 6
1 6.9
2 9
3 10.5
4 13
5 14.2
6 18
7 20.8
8 26
9 31.3
Use the graphing tool to plot the population data and determine the curve of best fit.
Part A
Question
What is the equation of the curve of best fit for the population data?
Enter the correct answer in the box by replacing a and b with the values from the graphing tool. Do not round the values of a and b.
Part B
Question
If the town continues to grow at the same rate, approximately what will be the population, to the nearest 100 people, 25 years after the town council started tracking the population data?
341,100 people
180,000 people
271,200 people
572,400 people
Question 2
Because of the growth in the town’s population, the agricultural department kept track of the town’s native bee population during the same time period. They feared with the increase of people in the town, the bee population would start to decrease, affecting the ecosystem. Their data is shown in the table.
Years Bee Population
(in thousands)
0 320
1 225
2 152.6
3 111.2
4 75
5 56.8
6 36.7
7 26.9
8 17.5
9 13.2
Use the graphing tool to plot the population data and determine the curve of best fit.
Part A
Question
What is the equation of the curve of best fit for the population data?
Enter the correct answer in the box by replacing a and b with the values from the graphing tool. Do not round the values of a and b.
Part B
After several years of recording the data, the agricultural committee requested help from the town council for a grant to boost the bee population. The council denied the request, saying it wouldn’t take any action until the population dropped below 5,000 bees.
In the 12th year after initially recording the bee population, the agricultural committee plans to speak with the board again. Will the committee have a good chance of convincing the board to help support bees this time around? Justify your conclusion using mathematical reasoning.
Answers
Answer:
1.The equation of best fit is ŷ = 2.69152X + 3.45818.
Step-by-step explanation:
For the town population data, the curve of best fit appears to be an exponential function of the form y = ab^x. Using the graphing tool, we can estimate the values of a and b to be:
a = 5.98
b = 1.121
Therefore, the equation of the curve of best fit is y = 5.98(1.121)^x.
For the bee population data, the curve of best fit also appears to be an exponential function of the form y = ab^x. Using the graphing tool, we can estimate the values of a and b to be:
a = 321.38
b = 0.675
Therefore, the equation of the curve of best fit is y = 321.38(0.675)^x.
Part B:
To find the population of the town 25 years after the council started tracking the population data, we can substitute x = 25 into the equation of the curve of best fit for the town population data:
y = 5.98(1.121)^25 ≈ 572,400
Therefore, the estimated population of the town 25 years after the council started tracking the population data is approximately 572,400 people.
For the bee population data, we can use the equation of the curve of best fit to predict the bee population in the 12th year after initially recording the data, which corresponds to x = 12.y = 321.38(0.675)^12 ≈ 2.92
Therefore, the estimated bee population in the 12th year after initially recording the data is approximately 2,920 bees (rounded to the nearest whole number).
Since the town council has set a threshold of 5,000 bees before taking action to support the bee population, it appears that the agricultural committee will not have a good chance of convincing the board to support bees this time around. The estimated bee population is well below the threshold set by the council, and it would take several years of significant growth for the bee population to reach that level. Therefore, the committee would need to provide strong evidence of the importance of bees to the ecosystem and the potential consequences of not taking action to support them in order to convince the board to change their stance.
Using the quadratic formula to solve 5x = 6x-
3, what are the values of x?
Answers
Answer:
x = -1
Step-by-step explanation:
Main goal move every variable towards the higher side which Makes it easier
5x-4 = 6x-3
Minus 5x on both sided
-4 = x -3
Add 3 on both sides
-1 = x
Find the perimeter of the figure shown above with aside length 5 unit
Answers
The perimeter of the figure with side length of 5 units is 50 units
How to determine the perimeter of the figureFrom the question, we have the following parameters that can be used in our computation:
Shape = rectangle
Smaller shapes = squares
Side lengths = 5 units
The perimeter of the figure is calculated as
Perimeter = Number of visible sides * Side length of the square shape
In this case, we have
Number of visible sides = 10
Substitute the known values in the above equation, so, we have the following representation
Perimeter = 10 * 5
Evaluate the products
Perimeter = 50 units
Hence, the perimeter is 50 units
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The numbers of customers that visited a store each hour for several hours after the store opened at 8 am are shown in the table. Hours after 8 am 1 3 4 6 9 Number of Customers 2 15 18 13 0 Which statement best describes the data?
Answers
The statement which best describes the data given is C) The data can be modeled by a quadratic function.
Given a data,
The numbers of customers that visited a store each hour for several hours after the store opened at 8 am are shown in the table.
It is clear that the number of customers increases to 18 for the first 4 hours and then decreases to 0 after 9 hours.
So this data cannot be modeled by a linear function or an exponential function.
Also since the number of customers arriving is not constant, this cannot be expressed as constant function.
So it is quadratic function.
Hence the correct option is c.
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The prism below has a base that is a regular pentagon whose perimeter is 25 feet and whose area is 43 squarefeet. The height of the prism is 11 feet. Which of the following is the volume of the prism?
Answers
The volume of a prism = Base area x Height
Base area = 43
Height = 11
Volume = 43 x 11
Volume = 473
Burning Brownie has five varieties of cakes as Chocolate fudge cake (Cake 1), Nutella-filled Cake (Cake 2), Marble Cake (Cake 3), Cheese cake (Cake 4) and Fruit Cake (Cake 5) at their store. The selling prices of each of the cakes are $9, $12, $4, $5, $8 respectively. a. Formulate the Revenue function If it takes 4 cups of milk, 7 cups of sugar, 1 egg, 3 cups flour & 4 cups cream to make Cake 1; 3 cups milk, 4 cups sugar, 2 egg, 4 cups flour & no cream to make Cake 2; 1 cups milk, 5 cups sugar, 3 eggs, 2 cups flour & 1 cup cream to make Cake 3; 5 cups milk, no sugar, 4 eggs, 4 cups flour & 5 cups cream for Cake 4; & lastly 4 cups milk, 8 cups sugar, 5 eggs, 6 cups flour & 3 cups cream to make Cake 5; Which types of cakes to be baked such that we get maximum Revenue? Keep in mind that the store has availability of maximum 280 cups milk, 300 cups sugar, 80 eggs, 250 cups flour & 190 cups cream at their disposal. b. Formulate the constraints of the scenario. c. Solve the system if linear inequalities using Excel Solver.
Answers
A. In equation form: Revenue = 9x1 + 12x2 + 4x3 + 5x4 + 8x5
B. Non-negativity constraint: x1, x2, x3, x4, x5 ≥ 0
How did we get these values?To solve this problem using E x c e l Solver, set up the revenue function and the constraints. Here's how you can do it:
a. Revenue Function:
Let's denote the number of cakes baked for each type as x1, x2, x3, x4, and x5 respectively.
The revenue function can be formulated as:
Revenue = (Selling Price of Cake 1 × Number of Cake 1) + (Selling Price of Cake 2 × Number of Cake 2) + (Selling Price of Cake 3 × Number of Cake 3) + (Selling Price of Cake 4 × Number of Cake 4) + (Selling Price of Cake 5 × Number of Cake 5)
In equation form:
Revenue = 9x1 + 12x2 + 4x3 + 5x4 + 8x5
b. Constraints:
The constraints for the availability of ingredients can be formulated as follows:
Milk constraint: 4x1 + 3x2 + x3 + 5x4 + 4x5 ≤ 280
Sugar constraint: 7x1 + 4x2 + 5x3 ≤ 300
Egg constraint: x1 + 2x2 + 3x3 + 4x4 + 5x5 ≤ 80
Flour constraint: 3x1 + 4x2 + 2x3 + 4x4 + 6x5 ≤ 250
Cream constraint: 4x1 + 5x3 + x4 + 3x5 ≤ 190
Non-negativity constraint: x1, x2, x3, x4, x5 ≥ 0
c. Solve the system of linear inequalities using E x c e l Solver:
To solve the system of linear inequalities using E x c e l Solver, follow these steps:
1. Open M i c r o s o f t E x c e l and enter the following data in a new sheet:
| | A | B |
|-----|-----------|-----------------|
| 1 | Cakes | Selling Price |
| 2 | Cake 1 | $9 |
| 3 | Cake 2 | $12 |
| 4 | Cake 3 | $4 |
| 5 | Cake 4 | $5 |
| 6 | Cake 5 | $8 |
| | | |
| | | Formula |
| 9 | Milk | 280 |
| 10 | Sugar | 300 |
| 11 | Eggs | 80 |
| 12 | Flour | 250 |
| 13 | Cream | 190 |
2. In cell B16, enter the formula for the revenue:
=B2×B7 + B3×B8 + B4×B9 + B5×B10 + B6×B11
3. In cell B18, enter the formula for the milk constraint:
=4×B2 + 3×B3 + B4 + 5×B5 + 4×B6
4. In cell B19, enter the formula for the sugar constraint:
=7×B2 + 4×B3 + 5×B4
5. In cell B20, enter the formula for the egg constraint:
=B2 + 2×B3 + 3×B4 + 4×B5 + 5×B6
6. In cell B21, enter the formula for the flour constraint:
=3×B2 + 4×B3 + 2×B4 + 4×B5 + 6×B6
7. In cell B22, enter the formula for the cream constraint:
=4×B2 + 5×B4 + B5 + 3×B6
8. In cell B24, enter the formula for the non-negativity constraint for Cake 1:
=B2
9. Repeat step 8 for the remaining cakes, entering the formulas in cells B25, B26, B27, and B28:
=B3
=B4
=B5
=B6
10. Now, select cells B16 to B28 and click on the "Solver" button in the "Data" tab.
11. In the Solver Parameters window, set the objective to maximize the cell B16 (Revenue).
12. Set the By Changing Variable Cells to B24:B28 (the number of cakes baked).
13. Click on the "Add" button in the "Subject to the Constraints" section.
14. In the Constraint window, select the range B18:B22 for the constraint cells.
15. In the Solver Parameters window, click on the "Add" button again and select the range B24:B28 for the non-negativity constraints.
16. Set the Solver options as desired, and click on the "Solve" button.
E x c e l Solver will calculate the optimal values for the number of cakes to be baked for each type that maximize the revenue, while satisfying the given constraints on ingredient availability. The solution will be displayed in cells B24:B28, indicating the number of cakes to be baked for each type.
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