Question

2. The Queen City Style Company makes several lines of skirts, dresses, and sport coats. Recently, a consultant suggested that the company reevaluate its South Islander line and allocate its resources to products that would maximize contribution to profits and to overhead. Each product requires the same polyester fabric and must pass through the cutting and sewing departments. The following data were collected for the study: Product Processing Time (hr) Material (yd) Max. Demand Cutting Sewing Skirt 1 1 1 - Dress 3 4 1 - Sport coat 4 6 4 150 The cutting department has 1000 hours of capacity, sewing has 1600 hours of capacity, and 800 yards of material are available. Each skirt contributes $8 to profits and overhead; each dress, $10; and each sport coat $35.

a. Specify the objective function and constraints for this problem and Use Excel Solver to solve the problem, and then generate Answer Report and Sensitivity Report. What is the best mix that maximizes the profit? What are the binding constraints?

Answer 1

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a. Specify the objective function and constraints for this problem.

?1 =number of skirts produced

?2 =number of dresses produced

?1 =number of sport coats produced

Maximize 8?1 + 10?2 + 35?3

subject to

?1 + 3?2 + 4?3 ≤ 1000

?1 + 4?2 + 6?3 ≤ 1600

?1 + ?2 + 4?3 ≤ 800

?3 ≤ 150

?1,?2, ?3 ≥ 0

Excel Solution:

Formulae:

Sensitivity Report:

Answer Report:

The optimal solution is ?1 = 100, ?2 = 100, ?3 = 150 with the maximum total profit of $7,050. (See the spreadsheet.)

Cutting time, material, and max demand are binding constraints. (The sewing constraint is not a binding constraint and has a slack of 200 hrs)

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