Question

In: Operations Management

Given the following problem answer the questions: A car manufacturer is producing new cars. The setup...

Given the following problem answer the questions:

A car manufacturer is producing new cars. The setup cost of the production facilities and the unit profit for each car are given below:

Toy   Setup cost ($)   Profit ($)

1     45000            12

2     76000            16

The company has two factories that are capable of producing these cars. In order to avoid doubling the setup cost only onefactory could be used.

The production rates of each car are given below (in units/hour):

            Car 1   Car2

Factory 1   52      38

Factory 2   42      23

Factories 1 and 2, respectively, have 480 and 720 hours of production time available for the production of these cars. The manufacturer wants to know whichof the new cars to produce, whereand how manyof each (if any) should be produced so as to maximize the total profit.

Question: Which one is the objective function?

Group of answer choices

1. max 12(x11+ x21) + 16(x12+ x22); where xij are production levels.

2. max 12(x11+ x21) + 16(x12+ x22) - 45000(f11 + f21) - 76000(f12 + f22); where f12 and f22 are binary variables and xij are production levels.

3. max 12(x1) + 16(x2) - 45000(f1) - 76000(f2); where f1 and f2 are binary variables and xij are production levels.

4. max 12(x1) + 16(x2); where xij are production levels.

Question: Which one includes some constraints of the problem?

f variables are binary and x variables are integer.

Group of answer choices

1. x1 <= (480/90) f1; x2 <= (720/65)f2

2. x1 <= 90 (480) f1; x2 <= 65 (720) f2

3. x11 <= (480/ 52) f11; x12 <=( 480/38) f12; x21 <= (720/42) f21; x22 <= (720/23) f22

4. x11 <= 52 (480) f11; x12 <= 38 (480) f12; x21 <= 42 (720) f21; x22 <= 23 (720) f22

Question: How many decision variables do we need to solve this problem?

Group of answer choices

2

8

6

Question: How many decision variables do we need to solve this problem?

Group of answer choices

2

8

6

Question: How many decision variables do we need to solve this problem?

Group of answer choices

2

8

6

Solutions

Expert Solution

Question: Which one is the objective function?

Group of answer choices

1. max 12(x11+ x21) + 16(x12+ x22); where xij are production levels.

2. max 12(x11+ x21) + 16(x12+ x22) - 45000(f11 + f21) - 76000(f12 + f22); where f12 and f22 are binary variables and xij are production levels.

3. max 12(x1) + 16(x2) - 45000(f1) - 76000(f2); where f1 and f2 are binary variables and xij are production levels.

4. max 12(x1) + 16(x2); where xij are production levels.

Correct answer is 2. max 12(x11+ x21) + 16(x12+ x22) - 45000(f11 + f21) - 76000(f12 + f22); where f12 and f22 are binary variables and xij are production levels.

reason : Above function correctly subtracts fixed cost from profit generated from production
Question: Which one includes some constraints of the problem?

f variables are binary and x variables are integer.

Group of answer choices

1. x1 <= (480/90) f1; x2 <= (720/65)f2

2. x1 <= 90 (480) f1; x2 <= 65 (720) f2

3. x11 <= (480/ 52) f11; x12 <=( 480/38) f12; x21 <= (720/42) f21; x22 <= (720/23) f22

4. x11 <= 52 (480) f11; x12 <= 38 (480) f12; x21 <= 42 (720) f21; x22 <= 23 (720) f22

Correct answer is 4. x11 <= 52 (480) f11; x12 <= 38 (480) f12; x21 <= 42 (720) f21; x22 <= 23 (720) f22

Question: How many decision variables do we need to solve this problem?

Group of answer choices

2

8

6

Correct answer is 8

Objective function is max 12(x11+ x21) + 16(x12+ x22) - 45000(f11 + f21) - 76000(f12 + f22); where f12 and f22 are binary variables and xij are production levels.

Here we can see number of binary an production varaibles are 8 which all are decision variables

keosha answered 4 months ago
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