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 1.50 3.00 2.00 B 2.00 1.00 2.50 с 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 $27 for product 1, $29 for product 2, and $32 for product 3. (a) Formulate a linear programming model for maximizing total profit contribution. (Let P, = units of product i produced, for i = 1, 2, 3.) Max s.t. Department A Department B Department P, P2, P, 20 (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 (in dollars)? (PP2, P3) - with profits (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, $590 for product 2, and $650 for product 3. If the solution developed in part (b) is to e used, what is the total profit contribution (in dollars) after taking into account the setup costs?

Answer 1

7 P, be the no q units of product produced P Produl 2 produced M Produt 3 produced paz (a) poft Conribution cire for produt 1 = $27 Produwt 2 - 829 Produs 3=832 + Max z = 27P, +29 P2 + 32 P₃ Srarment: 1.50p, + 3.opt a P3 5450 2p, + 1 p + 2.5pS 350 0.258,+ 0.2592 +0.25%; <50 P, P2P 30 (5) P. 60 P, 80 2 Profit totala $ 5860 Pa 20 Total set up costs 400+ (C) 590+ 650 = $1640 5860 - 1640 Final profit Excluding set up cost = 24-२२०

A B с D E F G 1 Labour Hrs Product 1 Product 2 Product 3 2 3.00 1.00 0.25 2.00 2.50 0.25 LHS 0 0 0 RHS 450 350 50 3 Department A 1.50 4 Department B 2.00 5 Department C 0.25 6 Labour Hrs 7 Department A 8 Department B 9 Department C 10 Profit 11 Product 1 27 12 Product 2 29 13 Product 3 32 14 15 Profit 0 No of products

A B C D F G 1 2. Product 1 Product 2 Product 3 E Labour Hrs LHS =$C$11*B3+$C$12*C3+$C$13*D3 =$C$11*B4+$C$12°C4+$C$13*D4 =$C$11*B5+$C$12*C5+$C$13*D5 3 RHS <= 450 <= 350 <= 150 2 2.5 0.25 1 0.25 3 Department A 1.5 4 Department B 2 5 Department C 0.25 6 7 Department A 8 Department B 9 Department C Labour Hrs 10 Profit No of products 11 12 13 14 15 Product 1 Product 2 Product 3 27 29 32 Profit =SUMPRODUCT(B11:B13,C11:C13)

Solver Parameters X Set Objective: $B$15 To: Max Min 0 O Value of: By Changing Variable Cells: $C$11:$C$13 Subject to the Constraints: SC$11:$C$13 = integer SES3:SE55 <= SGS3:SGS5 Add Change Delete 5 Reset All pr Load/Save Make Unconstrained variables Non-Negative Select a Solving Method: Simplex LP Options Solving Method Select the GRG Nonlinear engine for Solver Problems that are smooth nonlinear. Select the LP Simplex engine for linear Solver Problems, and select the Evolutionary engine for Solver problems that are non-smooth. 15 Help Solve Close

A ma C D E F G Labour Hrs 1 2. Product 1 Product 2 Product 3 3.00 1.00 0.25 2.00 2.50 0.25 LHS 450 350 50 RHS 450 350 50 3 Department A 1.50 4 Department B 2.00 5 Department C 0.25 Labour Hrs 7 Department A 8 Department B 9 Department C 10 Profit 11 Product 1 27 12 Product 2 29 13 Product 3 32 14 15 Profit 5860 No of products 60 80 60