Problem 7-11Hart 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: DepartmentProduct 1Product 2Product 3A1.503.002.00B2.001.002.50C0.250.250.25 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.A) Formulate a linear programming model for maximizing total profit contribution. For those boxes in which you must enter subtractive or negative numbers use a minus sign. (Example: -300)****I need help with Part E Only Please....Thanks**** Let P; = units of product i producedMaxV P1+V P3252830s.t.V P1+3 V P2|+2P3S1.54502P,|+1 V P2|+2.5 V P3s350.25 V P10.25P2 +0.25 V P3s50P1, P2, P3 2 0b. 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 =60P2 =80P3 =60Profit = $5540c. 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 $400for 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 = $3990 Vd. 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 thattakes 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. For thoseboxes in which you must enter subtractive or negative numbers use a minus sign. (Example: -300) Here introduce a 0-1 variable y, that is one if any quantity of product i is produced and zero otherwise.Маx25 V Pl+||28 V P2|+30 V P3|+-400 vy1+-550 V y2+-600 V y3s.t.1.5 V P1+3 V P2+2P3450 V2P1|+1 V P2|+2.5 V P3350 V0.25 V P1+.25P2 +0.25 V P350 V1 V P.-175 Vy1+1 V P2-150 V y21 V P3-140 V y3sP1, P2, P3 2 0; yı, Y2, Y3 = 0, 1e. 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 profitcontribution to that obtained in part (c).P1 =P2 =P3 =increasedProfit = $decreasedThe profit isby $

Name: Problem 7-11Hart Manufacturing makes three products. Each product requ
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Description: Problem 7-11Hart 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: DepartmentProduct 1Product 2Product 3A1.503.002.00B2.00

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Advanced Engineering Mathematics

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ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

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Problem 7-11

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:

Department	Product 1	Product 2	Product 3
A	1.50	3.00	2.00
B	2.00	1.00	2.50
C	0.25	0.25	0.25

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.

A) Formulate a linear programming model for maximizing total profit contribution. For those boxes in which you must enter subtractive or negative numbers use a minus sign. (Example: -300)

****I need help with Part E Only Please....Thanks****

Let P; = units of product i produced
Max
V P1+
V P3
25
28
30
s.t.
V P1+
3 V P2|+
2P3S
1.5
450
2P,|+
1 V P2|+
2.5 V P3s
350
.25 V P1
0.25P2 +
0.25 V P3s
50
P1, P2, P3 2 0
b. 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 =
60
P2 =
80
P3 =
60
Profit = $
5540
c. 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 = $
3990 V
d. 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. For those
boxes in which you must enter subtractive or negative numbers use a minus sign. (Example: -300)

Here introduce a 0-1 variable y, that is one if any quantity of product i is produced and zero otherwise.
Маx
25 V Pl+||
28 V P2|+
30 V P3|+
-400 vy1+
-550 V y2+
-600 V y3
s.t.
1.5 V P1+
3 V P2+
2P3
450 V
2P1|+
1 V P2|+
2.5 V P3
350 V
0.25 V P1+
.25P2 +
0.25 V P3
50 V
1 V P.
-175 Vy1
+
1 V P2
-150 V y2
1 V P3
-140 V y3s
P1, P2, P3 2 0; yı, Y2, Y3 = 0, 1
e. 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 =
P2 =
P3 =
increased
Profit = $
decreased
The profit is
by $

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