Question

(c) Suppose that 8, 6, and 8 hours of overtime may be scheduled in departments A, B, and C, respectively. The cost per hour of overtime is $18 in department A, $22.50 in department B, and $12 in department C. Formulate a linear programming model that can be used to determine the optimal production quantities if overtime is made available. What are the optimal production quantities, and what is the revised total contribution to profit? If required, round your answer to two decimal places. Product 1 Product 2 Production If required, round your answer to nearest whole number. Total Profit $ How much overtime do you recommend using in each department? If required, round your answer to two decimal places. If you answer is zero, enter "O OT hours: Used Dept. What is the increase in the total contribution to profit if overtime is used? If required, round your answer to nearest whole number.

Answer 1

a)

1188 Decision Variables Number of units of each product to be made Product1Product 2 No.of units 4 Objective function Maximize the total profit Constraints 9 1*B4+0.35 *C4 95 38 50 10 -0.3 B4+0.2*C4 11 0.2*B4+0.5*CA 12 13 14

1 Decision Variables Number of units of each product to be made Product 1 Product 2 4 No.of units 5 Objective function 6 Maximize the total profit C) Constraints 95 38 50 C) C) C) 10 12

Clear Solver Parameters to Set Objective To: ⓔMax OMin。Value Of: By Changing Variable Cells: SAS7 Subject to the Constraints: SAS9:SAS11SCS9:SCS11 Add Change Delete Reset All 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. Help Solve Clgse ее

1 Variables 2 Number of units of each product to be made Product 1 Product 2 4 No.of units 69.7772.09

Decision Variables Number of units of each product to be made Product 1 Product 2 69.7772.09 4 No.of units Objective function Maximize the total profit 3174.42 Constraints 95 35.35 50 95 38 50 10 12 13

b)

6 Variable Cells Final Value Reduced Objective Allowable Allowable Cell Coefficient Increase 0 0 Name 9 $B$4 No.of units Product 1 69.76744186 10 $C$4 No.of units Product 2 72.09302326 Cost Decrease 24 30 12.85714286 15 60 4.5 12 Constraints Final Value Shadow Constraint Allowable Allowable R.H. Side Increase Decrease 13 Price Cell Name 15 ŞA$9 Constraints 16 ŞA$10 Constraints 17 ŞA$11 Constraints 18 95 27.90697674 0 50 10.46511628 95 10.36363636 38 50 60 1E+30 2.651162791 31 35.34883721 12

Department A and Department C have positive shadow price. Therefore, they must be provided with overtime hours. Department A has higher shadow price.

Department A has a shadow price of 27.91.

>> Upper limit of what one would pay = $27.91

c)

Decision Variables Number of units of each product to be made Product 1 Product2 No.of units 4 Objective function Maximize the total profit 7 B4 30+C4 15-18*8-22.5 6-12 8 Constraints 9 1*B4+0.35 C4 10 -0.3 B4+0.2 C4 11 0.2*B4+0.5*CA 12 13 -95+8 -38+6

Decision Variables Number of units of each product to be made Product 1 Product 2 72.5686.98 4 No.of units Objective function 6 | Maximize the total profit 3106.40 Constraints 103 39.16 58 103 3 10 58 12

Product 1 ---> 72.56

Product 2--> 86.98

Total Profit --> $3106.40

>> OT hours used::

Department A = 103-95 = 8

Department B = 39.16-38 = 1.16

Department C = 58-50 = 8

>> Increase in profit = 3106.4 - 3174.42 = -$68.02