Question

I need (d) and (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 А. 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 $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/produced, for i = 1, 2, 3.) Max 27P, +29P2 +32P3 s.t. Department A 1.50P, +3P, +2P3 S 450 Department B2P + 1P2 + 2.5P3 < 350 Department c 0.25P+0.25P, +0.25P, S 50 P1, 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)? PPP) - 60.80,60 with profit $ 5860 (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 be used, what is the total profit contribution (in dollars) after taking into account the setup costs? $4220

Answer 1

(d)

Objective function

Max 27 P1 + 29 P2 + 32 P3 - 400 y1 - 590 y2 - 650 y3

additional constraints:

units of product 1 produced) P1 - 145 y1 <= 0

units of product 2 produced) P2 - 160 y2 <= 0

units of product 3 produced) P3 - 170 y3 <= 0

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

(e)

Solution of the mixed-integer program using LINDO is following:

Lingo 18.0 - Solution Report - Lingo1 File Edit Solver Window Help Lindo Model - Lingol Max 27P1+29P2+32P3-400yl-59072-650y3 s.t. Solution Report - Lingo1 Global optimal solution found. Objective value: Objective bound: Infeasibilities: Extended solver steps: Total solver iterations: Elapsed runtime seconds: 4610.000 4610.000 0.000000 3 14 0.42 Model Class : MILP 1.5P1+3P2+2P3<=450 2P1+1P2+2.5P3<=350 0.25P1+0.25P2+0.25P3<=50 Pl-14541 <=0 P2-160Y2 <=0 P3-170Y3 <=0 END INT yi INT v2 INT y3 Total variables: Nonlinear variables: Integer variables: 6 0 3 Total constraints: Nonlinear constraints: 7 0 Total nonzeros: Nonlinear nonzeros: 21 0 Variable Pl P2 P3 Y Y2 Y3 Value 100.0000 100.0000 0.000000 1.000000 1.000000 0.000000 Reduced Cost 0.000000 0.000000 0.000000 400.0000 590.0000 -86.66667 Row 1 2 3 4 5 6 Slack or Surplus 4610.000 0.000000 50.00000 0.000000 45.00000 60.00000 0.000000 Dual Price 1.000000 1.333333 0.000000 100.0000 0.000000 0.000000 4.333333 7

(P1, P2, P3, y1, y2, y3) = (100, 100, 0, 1, 1, 0) with profit $  4610