Problem II Cool Denim Company produces two items called Boot Jeans and Skinny Ja

Question

Problem II Cool Denim Company produces two items called Boot Jeans and Skinny Jackets. A unit of Boot Jeans requires 8 yards of denim and 2 pounds of R22 dye. A unit of Skinny Jackets requires 15 yards of denim and 3 pounds of R22 dye. The amount of cutting machine time needed on a unit of Boot Jeans is 1.5 hours, while the amount of cutting machine time needed on a unit of Skinny Jackets is 1 hour. The assembly time needed by a unit of Boot Jeans is 2.5 hours while the assembly time needed by a unit of Skinny Jackets is 1.75 hours. The amount of yards of denim available per production period is 280 yards. The company has secured 66 pounds of the special R22 dye for the production period. The company has three cutting machines which yield an effective combined time of 47 hours per production period. The total amount of assembly time available to the company per production period equals 130 hours. The company has received and accepted pre-production commitments of at least 5 units of Boot Jeans for the upcoming production period, and wants to keep production of Skinny Jackets to a maximum of 12 units in order not to overflow the market for the following period. The company cost accountants have determined that a single unit of Boot Jeans contributes $15 to profits, while a single unit of Skinny Jackets contributes $22 to profits. The company's objective is to maximize profit. If you are the production manager, how many units of Boot Jeans and Skinny Jackets should you produce so that the profit is maximized? 1. What are the decision variables (specify the units)? 2. What is the objective function? 3. Are there any redundant constraint(s)? Which one(s), if any? 4. Identify the corner points of the feasibility region. 5. What is the optimal production mix? 6. What is the optimal profit level? 7. If the manager is able to secure an additional pound of special R22 dye for S5/lb should it be bought? Why?

Explanation / Answer

The given question is a Linear Programming problem , where the objective of the firm is to maximise the profit of the firm through the optimal mix of Boot and Skinny Jeans.

Let X1, X2 represents Boot and Skinny Jeans.

The information on profit , raw material, machine time and assemblly is summarised in the table below.

The objective of the firm is to maximise the proft. So the objective function is

Solving the above with the help of MS Excel solver application, the solution is

Please note that the ansers to all questions included. A reductant solution is the one where RHS AND LHS are equal in constraint, which is marked in the solution, Otherwise non reduntant

Denim R22 Dye Cutting Machine time Assembly Time Profit Boot Jeans 8 2 1.5 2.5 15 Skinny Jeans 15 3 1 1.75 22 Availability 280 66 47 130 Demand Boot Jeans 5 Minimum Skinny 12 Maximum

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