Problem 8-1

Kelson Sporting Equipment, Inc., makes two different types of baseball gloves: a regular model and a catcher's model. The firm has 800 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)

ModelCutting and

Sewing

FinishingPackaging and

Shipping

Profit/GloveRegular model1/31/81$4Catcher's model3/21/41/2$7

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.LetR= number of units of regular model.C= number of units of catcher's model.MaxR+Cs.t.R+C- Select your answer -=Item 5Cutting and sewingR+C- Select your answer -=Item 9FinishingR+C- Select your answer -=Item 13Packing and ShippingR, C- Select your answer -=Item 150(b)Develop a spreadsheet model and find the optimal solution using Solver. How many gloves of each model should Kelson manufacture?Regular Model =unitsCatcher's Model =units(c)What is the total profit contribution Kelson can earn with the given production quantities?$(d)How many hours of production time will be scheduled in each department?DepartmentTime Used (Hours)Cutting and sewingFinishingPacking and Shipping(e)What is the slack time in each department?DepartmentSlack Time (Hours)Cutting and sewingFinishingPacking and Shipping