PLEASE answer question E!

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	1.60	3.10	2.10
B	2.20	1.20	2.70
C	0.35	0.35	0.35

During the next production period, the labor-hours available are 470 in department A, 370 in department B, and 70 in department C. The profit contributions per unit are $27 for product 1, $30 for product 2, and $32 for product 3.

1. 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) Let P_i = units of product i produced

   Max	fill in the blank 1P1	+	fill in the blank 2P2	+	fill in the blank 3P3
   s.t.
   	fill in the blank 4P1	+	fill in the blank 5P2	+	2.1P3		fill in the blank 6
   	2.2P1	+	fill in the blank 7P2	+	fill in the blank 8P3		fill in the blank 9
   	fill in the blank 10P1	+	0.35P2	+	fill in the blank 11P3		fill in the blank 12
   P1, P2, P3 0

2. 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
3. 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 $420 for product 1, $570 for product 2, and $620 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
4. 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 185 units of product 1, 160 units of product 2, or 150 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_i that is one if any quantity of product i is produced and zero otherwise.

   Max

   fill in the blank 18P1

   +

   fill in the blank 19P2

   +

   fill in the blank 20P3

   +

   fill in the blank 21y1

   +

   fill in the blank 22y2

   +

   fill in the blank 23y3

   s.t.

   fill in the blank 24P1

   +

   fill in the blank 25P2

   +

   2.1P3

   fill in the blank 26

   2.2P1

   +

   fill in the blank 27P2

   +

   fill in the blank 28P3

   fill in the blank 29

   fill in the blank 30P1

   +

   0.35P2

   +

   fill in the blank 31P3

   fill in the blank 32

   fill in the blank 33P1

   +

   fill in the blank 34y1

   fill in the blank 35

   fill in the blank 36P2

   +

   fill in the blank 37y2

   fill in the blank 38

   fill in the blank 39P3

   +

   fill in the blank 40y3

   fill in the blank 41

   P1, P2, P3 0; y1, y2, y3 = 0, 1

5. 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

   increaseddecreased

   by $ fill in the blank 47.