Question

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	2.00	1.50	3.00
B	2.50	2.00	1.00
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 $30 for product 1, $25 for product 2, and $28 for product 3.

Solve the linear program formulated in part (a). How much of each product should be produced, and what is the projected total profit contribution?
	Product 1 Product 2 Product 3 Amount to Produce
	Profit $
(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?
	$
(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 provided in part (c) 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. What are the new objective function and additional equation constraints?
	If the constant is "1" it must be entered in the box.
	Let Yi is one if any quantity of product i is produced and zero otherwise.
	Max $ P1 + $ P2 + $ P3 - $ Y1 - $ Y2 - $ Y3 s.t. P1

			Y1
	P2

			Y2
	P3

Y3 P1, P2, P3 ≥ 0
(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).
	If required, round your answers to nearest whole number. If your answer is zero enter “0”.
	Product 1 Product 2 Product 3 Amount to Produce
	Updated Profit $

Answer 1

Answer: Date: ----9/5/2019 In the optimal solution, we have gotten Product 1 and 3 positive optimal solutions and Product 2 is zero. Therefore, the values of Y1 and Y3 are 1 and Y2-0. So, the profit must be 30 109.09 25*0 28*77.27 -4001- 550*0-6001 $4,436 LINDO code Max 30P125P2 28P3 - 400Y1 - 550Y2 -60OY3 s.t. P1-175Y1<0 P2-150Y2 0 P3-140Y30 2.00P1 1.50P2 3.00P3<450 2.50P1 2.00P2 1.00P3<350 0.25P1 0.25P2 0.25P3 <50 tnKd INT Y1 INT Y2 INT Y3

Solution Global optimal solution found. Objective value: Objective bound: Infeasibilities: Extended solver steps: Total solver iterations Elapsed runtime seconds: 4436.364 4436.364 0.000000 14 0.06 Model Class: MILP Total variables: Nonlinear variables: Integer variables: Total constraints: 7 Nonlinear constraints: 21 TotaI nonzeroS: Nonlinear nonzeros Variable Pl P2 P3 Yl Y2 Y3 Value 109.0909 0.000000 77.27273 1.000000 0.000000 1.000000 If this answer is not coming correct, one should contact the instructor to correct the entry in the software system. The above solution is correct.

tf the constant is "1 it must be entered in the box. If required, round your answers to two decimal places Let P units of product i produced Max 30 2P28 OP s.t. 450 50 b) Solve the linear program formulated in part (a). How much of each product should be produced, and what is the projected total profit contibution? Product 1 Product 2 Product 3 Amount to Produce Profits ร540 c) After evaluating the solution obtained in part (b), one of the production supervisors noted that production setup costs had not been talken 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 taling into account the setup costs? 3990 d) Management realzed that the optimal product mi, takdng setup costs into account, might be different from the one recommended in part (b). Formulate a moxed-integer linear program that takes sebup costs provided in part (c) irto account. Management aiso 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. What are the new objective function and addrional equstion constraints? If the constant is " it must be entered in the box Let Y, is one if any quanbty of product i is produced and zero otherwise. Max s.t. 175 150 y 14 vs e) selve the mixed-integer hnear program formulated in part (a). How much of each product should be produced and what is the projected total profit contnibution? compare this profit contnbution to that cbtained in part (c). If required, round your answers to nearest whole number. if your answer is zero enter o Product 1 Product 2 Product 3 Amount to Produce