1. Problem 3-05

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

Letting
	R = number of regular gloves
	C = number of catcher's mitts
leads to the following formulation:

	Max	5R + 8C
	s.t.
		R + C	? 900	Cutting and sewing
		R + C	? 300	Finishing
		R + C	? 100	Packaging and shipping
R, C ? 0

The sensitivity report is shown in the 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

a. What is the optimal solution, and what is the value of the total profit contribution?

	Optimal Solution
Regular Glove
Catcher's Mitt
Total Profit	$

c.

d. Which constraints are binding or non biniding

Cutting and Sewing:
Finishing:
Packaging and shipping:

e.

f. What are the shadow prices for the resources?

Cutting and Sewing:
Finishing:
Packaging and shipping:

g. Interpret each. ( the answer that it could be are highlighted in yellow. ) The shadow price is the value that the ( A. Objective function , B. Variables R and C. Slack or surplus D. Constraints 1, 2, 3 ) will change by if you increase the constraint by one unit. Cutting and sewing has a shadow price of ( A. 0 , B. 3 , C. 28 , D. 175 ) which means that if we add one hour to the cutting and sewing department the value of the objective function would (A. Not change , B. Increase by $3, C. Increase by $28, D. Increase by $175) . Finishing has a shadow price of (A. 0, B. 3, C. 28, D. 175) which means that if we add one hour to the finishing department the value of the objective function would ( A. Not change , B. Increase by $3, C. Increase by $28 , D. Increase by $175)

Packaging and shipping has a shadow price of (A. 0, B. 3, C. 28, D. 175) which means that if we add one hour to the packaging and shipping department the value of the objective function would ( A. not change , B . Increase by $3, C. Increase by $28, D. Increase by $175 Constraints with a shadow price of 0 means that ( A. it is a binding constraint, B. it is a nonbinding constraint, C. A mistake has been made, D. 0 hours that constraints are used)

h. If overtime can be scheduled in one of the departments, where would you recommend doing so?

A. Cutting and sewing

B. Finishing

C. Packing and shipping