A manufacturing company produces 3 different products A, B, and C. Three types of components, i.e., X, Y, and Z, are used in the production of these products. One unit of product A requires 2 units of X, 2 units of Y, and 2 units of Z. One unit of product B requires 1 unit of X, 3 units of Y, and 2 units of Z. One unit of product C requires 1 unit of X, 2 units of Y, and 3 units of Z.Currently, the company has no existing inventory of the components. The company can purchase X at the price of $20 per unit but no more than 300 units due to the supplier's limited capacity constraint. The company can purchase Y at the price of $30 per unit without any upper limit. The company can purchase Z at the full price of $25 per unit for the first 100 units but the per unit price drops to $20 for the remaining units if any i.e., the purchase quantity in excess of 100 units). The market prices of the three products are $200 for A, $240 for B and $220 for C. The company knows that the demand for products A, B, and Care equal to 100, 80, and 90 units, respectively. Therefore, the company should not produce more than the demand for each product. However, the company incurs a per unit penalty of $40 for any unsatisfied demand. The company needs to decide the component płarchase plan and the production mix decisions to maximize its profits subject to all the business constraints described above. Formulate the company's problem as an optimization problem, i.e., providing the mathematical expressions for the decision variables, the objective function, and the constraints.

Answer:

Step-by-step explanation:

Using the Excel Formula:

Decision    Variable        Constraint              Constraint

A                     65                          65                         100

B                     80                          80                         80

C                     90                         90                          90

                      14100                    300                        300

= (150 *B3)+(80*B4) +(65*B5)-(100-B3+80-B4+90-B5)*90

Now, we have:

Suppose A, B, C represent the number of units for production A, B, C which is being manufactured

                             A              B                  C                Unit price

Need of X          2                 1                   1                     $20

Need of Y           2                3                  2                    $30

Need of Z           2                2                  3                    $25

Price of  

manufac -      $200          $240            $220      

turing

Now,  for manufacturing one unit of A, we require 2 units of X, 2 units of Y, 2 units of Z are required.  

Thus, the cost or unit of manufacturing of A is:

$20 (2) + $30(2) + $25(2)

$(40 + 60 + 50)

= $150

Also, the market price of A = $200

So, profit = $200 - $150 = $50/ unit of A

Again;

For manufacturing one unit of B, we require 1 unit of X, 3 units of Y, and 2 units of Z are needed and they are purchased at $20, $30, and 425 each.

So, total cost of manufacturing a unit of B is:

= $20(1) + $30(3) + $25(2)

= $(20 + 90+50)

= $160

And the market price of B = $240

Thus, profit = $240- $160  

profit = $80

For manufacturing one unit of C, we have to use 1 unit of X, 2 unit of Y, 3 units of Z are required:

SO, the total cost of manufacturing a unit of C is:

= $20 (1) + $30(2) + $25(3)

= $20 + $60 + $25

= $155

This, the profit = $220 - $155 = $65

However; In manufacturing A units of product A, B unit of product B & C units of product C.

Profit  --> 50A + 80B + 65C

This should be provided there is no penalty for under supply of there is under supply penalty for A, B, C is $40

The current demand is:

100 - A

80 - B

90 - C respectively

So, the total penalty

[tex]{(100 - A) + (80 - B) +(90 - C) } + \$40[/tex]

This should be subtracted from profit.

So, we have to maximize the profit  

[tex]Z = 50A + 80B + 65C = {(100 -A) + (80 - B) + (90 - C)};[/tex]

Subject to constraints;

we have the total units of X purchased can only be less than or equal to 300 due to supplies capacity

Then;

[tex]2A + B +C \le 300[/tex] due to 2A, B, C units of X are used in manufacturing A, B, C units of products A, B, C respectively.

Next; demand for A, B, C will not exceed 100, 80, 90 units.

Hence;

[tex]A \le 100[/tex]

[tex]B \le 80[/tex]

[tex]C \le 90[/tex]

and [tex]A, B, C \ge 0[/tex] because they are positive quantities

The objective is:

[tex]\mathbf{Z = 50A + 80B + 65 C - (100 - A + 80 - B + 90 - C) * 40}[/tex]

A, B, C [tex]\to[/tex] Decision Varaibles;

Constraint are:

[tex]A \le 100 \\ \\ B \le 100 \\ \\ C \le 90 \\ \\2A + B + C \le 300 \\ \\ A,B,C \ge 0[/tex]

The sum of seven and x

For 120 consecutive days, a process engineer has measured the temperature of champagne bottles as they are made ready for serving. Each day, she took a sample of 8 bottles. The average across all 960 bottles (120 days, 8 bottles per day) was 46 degrees Fahrenheit. The standard deviation across all bottles was 0.8 degrees Fahrenheit. what would be the center line

If the manager sold 15 corn dogs, how would this quantity be represented in her table?

A marketing research firm believes that more than half of adults drink mostly either regular or diet soda. To test this claim, Gallup took a nationally representative sample of 2027 adults and asked them about their soda consumption. The survey shows that 950 of those surveyed drink mostly either regular or diet soda. The test statistics for the above hypthesis test for the proportion of adults who drink mostly either regular or diet soda is:________. (Round your answer to two decimal places)

do anybody know how to help me cause i really need it right now.

I NEED HELP ON A PROBLEM FAST!!​

15a > 75. Substitute 5 for a. PLEASE HELP

three times the sum of 14 and number (x).​

Please round to nearest hundredth and give explanation.

May someone pls help me with this question

Two brothers have a total age of 28 if one brother is older by 20 years how old is the second brother

area of the algebra tiles as a sum

Which three steps are correct when solving this quadratic equation by completing the square? X^2-10x=39

Suppose it is known that 23% of students at a certain college participate in a textbook recycling program each semester. Complete parts (a) and (b) below. a. If a random sample of 40 students is selected, do we expect that exactly 23% of the sample participates in the textbook recycling program? Why or why not? Choose the correct answer below. A. We expect that exactly 23% of the sample participates in the textbook recycling program, because that is the percentage of students that participate in the program regardless of sample or population size B. We expect that exactly 23% of the sample participates in the textbook recycling program, because a sample always has the same statistics as the population C. We do not expect that exactly 23% of the sample participates in the textbook recycling program. 23% is a population statistic and you cannot know anything about a sample from the population D. We do not expect that exactly 23% of the sample participates in the textbook recycling program. We do expect that the sample proportion will be close to the population proportion, but it will vary by the sample error from sample to sample b. Suppose we take a sample of 400 students and find the sample proportion participating in the recycling program. Which sample proportion do you think is more likely to be doser to 23% the proportion from a sample size of 40 or the proportion from a sample size of 400? Explain your reasoning. Choose the correct answer below A. The sample with size 40 will be closer to 23% because a smaller sample size has a smaller standard error B. The sample with size 400 will be closer to 23% because a larger sample size has a smaller standard error. C. The sample with size 400 will be closer to 23% because a larger sample size has more variation, D. The sample with size 40 wil be closer to 23% because a smaller sample size has loss variation

A can of paint is a right circular cylinder. The radius of the base is 5 centimeters and the height is 12 centimeters. Find the number of cubic centimeters of paint, in terms of π, contained in a full container.

Please Help!!! I'll Give Best And Brainliest if it lets me!

Explain why (x+1)(3x-6) is NOT a complete factorization of 3x^2-3x-6

okay so for the 3 and for its 3 to the 4th power btw
3^4+ 2 ⋅ 5 = ____. (Input whole numbers only.)

{{{{{{{{{{{{{{{{{{{{{ HELP QUICK }}}}}}}}}}}}}}}}}}}}}}}}

If I had to find the perimeter of triangle, I would:

Group of answer choices

take the square root of the hypotenuse

multiply all sides together

Add all three side measures together

apply the formula for circumference

Use the data on the dot plot to answer the question.​

Can someone help me plz? I’ll reward points + brainalist

Find the area of each triangle o the nearest tenth.

I'm terrible at fractions I need help​

Please I need help really fast

3 x 3 x 3 x 3 x 3 x 3 as an exponential notation

Explain how to solve the equation.

Find the radius of a circle in which the central angle, a, intercepts an arc of the given length
a = 30°, s = 9in

PLEASE HELP 20 POINTS
1 Which parallelograms have congruent diagonals?

only squares

squares and rectangles

squares and rhombuses

squares, rectangles, and rhombuses

2. Which parallelograns have perpendicular diagonals?

only squares

squares and rectangles

squares and rhombuses

squares, recangles, and rhombuses​

Help please plzzzzzzzz

A movie theater offers many movie selections for its customers. The table below shows a summary of five movies currently offered and whether the movie is appropriate for children.

A 5-column table with 5 rows. Column 1 is labeled Title with entries The Davis Family, Hill House, Danger Zone, Mixed Bag, Closure. Column 2 is labeled Movie Type with entries comedy, drama, drama, comedy, drama. Column 3 is labeled length (minutes) with entries 92, 87, 123, 91, 100. Column 4 is labeled Critics' score with entries 78.2, 45.7, 56.0, 71.8, 67.2. Column 5 is labeled audience with entries adult, youth, adult, youth, adult.

What are the individuals in the data set?

movie titles
movie types
lengths
critics’ scores