3 of 8 3. Telson Sporting Equipment makes two different types of baseball gloves

Question

3 of 8 3. Telson Sporting Equipment makes two different types of baseball gloves: a regular model and a catcher's model. The firm has 900 hours of production time available in its cutting and sewing department, 300 hours available in its finishing department, and 6000 minutes available in its packaging and shipping department. The production time requirements and the revenue contribution per glove are given in the following table: TABLE 1 Production Time (hours) Model Cutting & Sewing Finishing Packaging & Shipping Revenue/Glove 1 1/2 1/s Regular Model 14 ss 3/2 1/3 Catcher's Model a) Formulate a Linear Programming model to maximize total revenue. Give clear, numeric definitions of your decision variables. 3 21% D

Explanation / Answer

a) Decision Variables will be the number of Regular model gloves and number of ctcher's model gloves that the company should manufacture to maximie its revenue.

Let's say number of regular model gloves are R and number of catcher's model gloves are C

First of all, we will write the objective function:

Max Z = 5R + 8C

Now, the constraints

1R + 3/2C 900 [Available time on cutting and sewing department]

1/2R + 1/3C 300 [Available time on finishing department]

1/8R + 1/4C 100 [Available time on packaging and shipping department]

R, C 0 [Both the decision variables should be non-negative]

b.) (i) Optimal Solution:

R = 500; C = 150

Optimal Value:

Z = 500*5 + 150*8 = $3700

(ii) Optimal solution will remain the same because allowable increase is 2 for catcher's model, which mean optimal solution will remain some untill the price of catcher's model go above $10.

Hence, optimal solution:

R = 500; C = 150.

But, the optimal value of revenue will change:

Z = 500*5 + 150*9 = 3850

(iii.) Similar to previous part, here the optimal solution will not change because the allowable decrease is $1 which means the optimal solution will not change until the revenue/glove for regular model goes below $4.

(iv.) Similar to previous part, here the optimal solution will not change because the allowable decrease is 166.67 which means the optimal solution will not change until the available hours for finishing department go below 133.33 hours.

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