(Solution) : Kelson Sporting Equipment, Inc., makes two different types


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Kelson Sporting Equipment, Inc., makes two different types of baseball gloves: a regular model and a catcher’s model. The firm has 700 hours of production time available in its cutting and sewing department, 300 hours available in its finishing department, and 200 hours available in its packaging and shipping department. The production time requirements and the profit contribution per glove are given in the following table:

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Production Time (Hours) Model Cutting and Sewing Finishing Packaging and Shipping Profit/Glove Regular model 1 3/2 1/6 $4 Catcher’s model 3/2 1/2 1/2 $8 Assuming that the company is interested in maximizing the total profit contribution, answer the following:

(a) What is the linear programming model for this problem? If required, round your answers to 3 decimal places or enter your answers as a fraction. Let R = number of units of regular model. C = number of units of catcher’s model.

Max 4 R + 8 C s.t. 1 R + 3/2 C 700

Cutting and sewing 3/2 R + 1/2 C 300 Finishing 1/6 R + 1/2 C 200

Packing and Shipping R, C 0

(b) Develop a spreadsheet model and find the optimal solution using Solver. How many gloves of each model should Kelson manufacture?

Regular Model = 75 units Catcher’s Model = 375 units

(c) What is the total profit contribution Kelson can earn with the given production quantities? $ 3300

(d) How many hours of production time will be scheduled in each department?

Department Time Used (Hours) Cutting and sewing 637.5 Finishing 300 Packing and Shipping 200

(e) What is the slack time in each department? Department Slack Time (Hours)

Cutting and sewing ??????????????

Finishing Packing ??????????????

Shipping ??????????????

Expert Answer


Kelson Sporting Equipment, Inc., makes two different types of baseball gloves: a regular model and a catcher’s model. The firm has 700 hours of produc

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