Question

3. FinFone Paper Mill is a small-scale paper making company which has four making machines to produce four different types of papers. Each type of paper must go through processing on each of four machines. The manufacturing time (in minutes) per unit of paper produced is in the following table 16 2.5 0.9 2.5 2.6 6.5 The maximum time allotted for each machine is 30 hours per week and at least 100 units of each type of paper should be made using these machines during the week Profit per unit is: 032 0.44 0.5 1. Develop a linear programming model for this problem (Excel) 2. What are the decision variables for this problem? Paper types ABC& D 3. What is the optimal solution in terms of the objective function and decision A 100 B- 100 C- 203 D- 100 Pe 195.38 4. Is there only one optimal solution for this problem? Yes/No and briefly explain. Hint: Solver is not required to answer this question. Yes, because the constraint line is not parallel to any of the objective function

Answer 1

1) and 2) and 3)

xSUMPRODUCT (D4:G4,SD$3:$G$3) Maximum Total Time Time (mins) alloted No. of papers of each Type Objective Value 100 100 203 100 mins 1800 1800 Time on machine 1 Time on machine 2 Time on machine 3 Time on machine 4 Profit per paper 2.4 1.2 2.4 0.9 2.5 0.32 2.7 3.2 3.3 5.1 6.5 0.5 1228.1 1429.6 1287.8 1799.6 196.32 2.1 3.2 2.5 3.2 0.44 0.25

Obiective Cell (Max Constraints Driginal Valu 183.9 Cell Name Cell Name Cell Value Formula Status Slack Su$4 Variable Cells Time on machine 1 Objective 196.32 SH$4 SH$5 SH$6 SH$7 Time on machine 1 Total Time 1228.1 SH$A SISA Not Binding Time on machine 2 Total Time 1429.6 SH$5 I$5 Not Binding Time on machine 3 Total Time 1287.8 $H$6 I$6 Not Binding Time on machine 4 Total Time 1799.6 $H$7IS7 Not Bindin 571.9 370.4 512.2 0.4 Cell Name riginal Value Final Value Integer SD$3 SES3 SF$3 SG$3 No. of papers of each Type A No. of No. of No. of papers of each Type D 100 110 150 100 110 203 Integer 120 100 Integer Integer Integer of each Tvpe B SD$3:$G$3 100 SD$3 SE$3 SF$3 SGS3 of each Type C No. of papers of each Type A No. of papers of each Type B No. of No. of 100 SD$3 100 Binding 100 $E$3100 Bindin 203 SF$3-100 Not Bindi 100 SGS3-100 Bindin of each Type C of each Type D 103 0 SD$3:SGS3-Integer
Your answers to problem 2 and 3 are correct except the optimal value i.e Profit = 196.32.

4). Yes because the objective function is not parallel to any constraint.