Question

24. Kelson Sporting Equipment, Inc., 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 100 hours available in its packaging and shipping department. The production time requirements and the profit contribution per glove are given in the following table: Production Time (hours) Cutting Packaging and Sewing Finishing and Shipping Profit/Glove Model Regular model Catcher's model $5 $8 Assuming that the company is interested in maximizing the total profit contribution, an- swer the following: a. What is the linear programming model for this problem? b. Find the optimal solution using the graphical solution procedure. How many gloves of each model should Kelson manufacture? c. What is the total profit contribution Kelson can car with the given production quantities? d. How many hours of production time will be scheduled in each department? e. What is the slack time in each department?

Answer 1

Let number of units or regular model be x and catcher model be y

We need to maximise profits=max(5x+8y)

subject to

$1x+1.5y\leq900$

$\frac{x}{2}+\frac{y}{3}\leq 300$

$\frac{x}{8}+\frac{y}{4}\leq 100$

and x,y are integers

We get x=500,y=150

c)Profit=500*5+8*150=3700

d)Cutting and Sewing->725hrs

Finishing->300hrs

Packaging and Shipping->100hrs

e)Slack time is observed only in Cutting and Sewing department->900-725=175hrs

Other departments are neck to neck.