Question 3 - Linear Programming (10 Marks)

Dotti sells a range of women's jackets. The following presents hypothetical information in regards to biker jacket, bomber jacket and denim jacket varieties. Arnold, the production manager of the manufacturer which supplies these jackets to Dotti, would like you to assist him in identifying the optimal production mix. Below is an estimation of the costs to manufacture these three styles of jackets.

Biker jacketsBomber jacketsDenim jacketsSelling Price$40.00$35.00$35.00Costs:Raw materials$10.00$9.00$13.75Direct labour$8.00$7.15$6.00Variable overhead$4.00$3.58$3.00Fixed overhead$0.80$0.72$0.60

Each of the three products goes through the same manufacturing process. The time for each process and the hours available each month is provided in the table below.

Fabric PreparationPattern CuttingStitchingInspection and PackagingBiker jackets0.30.150.350.1Bomber jackets0.250.150.350.1Denim jackets0.20.10.250.1Hour available per month1,1006001,500500

Required:

1. Using Excel Solver, formulate a linear program to determine the optimal mix of jacket varieties each month which ensures that the maximum contribution margin is obtained (6 Marks).
2. Discuss your results and suggest possible ways in which the firm could improve their profitability in light of the Solver analysis (4 Marks).

Ensure that your answers for the above are discussed and supported by relevant calculations/workings.

Question 3 - Linear Programming (10 Marks) Dotti sells a range of women's jackets. The following presents hypothetical information in regards to biker jacket, bomber jacket and denim jacket varieties. Arnold, the production manager of the manufacturer which supplies these jackets to Dotti, would like you to assist him in identifying the optimal production mix. Below is an estimation of the costs to manufacture these three styles of jackets. Biker jackets Selling Price Costs: Raw materials Direct labour Variable overhead Fixed overhead Bomber jackets Denim jackets $40.00 $35.00 $35.00 $10.00 $8.00 $9.00 $7.15 $13.75 $6.00 $4.00 $3.58 $3.00 $0.80 $0.72 $0.60 Each of the three products goes through the same manufacturing process. The time for each process and the hours available each month is provided in the table below. Biker jackets Bomber jackets Denim jackets Hour available per month Fabric Preparation 0.3 0.25 0.2 1,100 0.15 0.15 0.1 0.35 0.35 0.25 Inspection and Packaging 0.1 0.1 0.1 600 1,500 500 Pattern Cutting Stitching Required: 1. Using Excel Solver, formulate a linear program to determine the optimal mix of jacket varieties each month which ensures that the maximum contribution margin is obtained (6 Marks). 2. Discuss your results and suggest possible ways in which the firm could improve their profitability in light of the Solver analysis (4 Marks). Ensure that your answers for the above are discussed and supported by relevant calculations/workings