Formulate a linear programming model. Hart Manufacturing makes three products. Each product requires manufacturing operations in three departments: A, B, and C. The labor-hour requirements, by department, are as follows:

During the next production period, the labor-hours available are 450 in department A, 350 in department B, and 50 in department C. The profit contributions per unit are $25 for product 1, $28 for product 2, and $30 for product 3.

Formulate a linear programming model for maximizing total profit contribution. If required, round your answers to two decimal places. For those boxes in which you must enter subtractive or negative numbers use a minus sign. (Example: -300)

Let Pi = units of product i produced

Max fill in the blank 1

P1 + fill in the blank 2

P2 + fill in the blank 3

P3

s.t.

fill in the blank 4

P1 + fill in the blank 5

P2 + 2P3 ≤ fill in the blank 6

2P1 + fill in the blank 7

P2 + fill in the blank 8

P3 ≤ fill in the blank 9

fill in the blank 10

P1 + .25P2 + fill in the blank 11

P3 ≤ fill in the blank 12

P1, P2, P3 ≥ 0

Solve the linear program formulated in part (a). How much of each product should be produced, and what is the projected total profit contribution?

P1 = fill in the blank 13

P2 = fill in the blank 14

P3 = fill in the blank 15

Profit = $ fill in the blank 16

After evaluating the solution obtained in part (b), one of the production supervisors noted that production setup costs had not been taken into account. She noted that setup costs are $400 for product 1, $550 for product 2, and $600 for product 3. If the solution developed in part (b) is to be used, what is the total profit contribution after taking into account the setup costs?

Profit = $ fill in the blank 17

Management realized that the optimal product mix, taking setup costs into account, might be different from the one recommended in part (b). Formulate a mixed-integer linear program that takes setup costs into account. Management also stated that we should not consider making more than 175 units of product 1, 150 units of product 2, or 140 units of product 3. If required, round your answers to two decimal places. For those boxes in which you must enter subtractive or negative numbers use a minus sign. (Example: -300) Here introduce a 0-1 variable yi that is one if any quantity of product i is produced and zero otherwise.

Max fill in the blank 18

P1 + fill in the blank 19

P2 + fill in the blank 20

P3 + fill in the blank 21

y1 + fill in the blank 22

y2 + fill in the blank 23

y3

s.t.

fill in the blank 24

P1 + fill in the blank 25

P2 + 2P3 ≤ fill in the blank 26

2P1 + fill in the blank 27

P2 + fill in the blank 28

P3 ≤ fill in the blank 29

fill in the blank 30

P1 + .25P2 + fill in the blank 31

P3 ≤ fill in the blank 32

fill in the blank 33

P1 + fill in the blank 34

y1 ≤ fill in the blank 35

fill in the blank 36

P2 + fill in the blank 37

y2 ≤ fill in the blank 38

fill in the blank 39

P3 + fill in the blank 40

y3 ≤ fill in the blank 41

P1, P2, P3 ≥ 0; y1, y2, y3 = 0, 1

Solve the mixed-integer linear program formulated in part (d). How much of each product should be produced, and what is the projected total profit contribution? Compare this profit contribution to that obtained in part (c).

P1 = fill in the blank 42

P2 = fill in the blank 43

P3 = fill in the blank 44

Profit = $ fill in the blank 45

The profit is

by $ fill in the blank 47

.

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