Question

use Excel Screen shot Pleaseeeee 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) Model Cutting and Sewing Finishing Packaging and Shipping Profit/Glove Regular model 1 1/2 1/8 $5 Catcher's model 3/2 1/3 1/4 $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? Enter the answers as fractions or round the answers to 3 decimal places. If the constant is "1" it must be entered in the box. Do not round intermediate calculation. If an amount is zero, enter "0". Let R = number of units of regular model. C = number of units of catcher's model. Max R + C s.t. R + C Cutting and Sewing R + C Finishing R + C Packing and Shipping R, C (b) Develop a spreadsheet model and find the optimal solution using Solver. How many gloves of each model should Kelson manufacture? Regular Model = units Catcher'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? Department Time Used (Hours) Cutting and Sewing Finishing Packing and Shipping (e) What is the slack time in each department? If your answer is zero, enter “0”. Department Slack Time (Hours) Cutting and Sewing Finishing Packing and Shipping

Answer 1

Let R= number of units of regular model.

C= number of units of catcher’s model

Max 5R + 8C

s.t
R +3/2C <= 900 (Cutting and sewing)

1/2 R + 1/3 C <= 300 (Finishing)

1/8 R+ 1/4 C<=100 (Packing and shipping)

R, C>=0

b)

he sensitivity report is shown in figure below.

FIGURE: THE SOLUTION FOR THE KELSON SPORTING EQUIPMENT PROBLEM

Optimal Objective Value =       3700.00000
		Variable		Value		Reduced Cost
		R		500.00000		0.00000
		C		150.00000		0.00000
		Constraint		Slack/Surplus		Dual Value
		1		175.00000		0.00000
		2		0.00000		3.00000
		3		0.00000		28.00000

		Variable		Objective Coefficient		Allowable Increase		Allowable Decrease
		R		5.00000		7.00000		1.00000
		C		8.00000		2.00000		4.66667
		Constraint		RHS Value		Allowable Increase		Allowable Decrease
		1		900.00000		Infinite		175.00000
		2		300.00000		100.00000		166.66667
		3		100.00000		35.00000		25.00000

regular = 500
catchers = 150

c)
37000

d)
cutting and sewing - 725
finishing - 300
shipping - 100

e)
slack for cutting and sewing is 175
other two have slack= 0

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