Question Content Area

Problem 3-06 (Algorithmic)

Kelson Sporting Equipment, Inc., makes two different types of baseball gloves: a regular model and a catcher's model. The firm has 700 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	$7
Catcher`s model	10/3	1/3	1/5	$10

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

	Max	7R + 10C
	s.t.
		R + 10/3 C	700	Cutting and sewing
		1/2 R + 1/3 C	300	Finishing
		1/8 R + 1/5 C	100	Packaging and shipping
R, C 0

The sensitivity report is shown in figure below.

Optimal Objective Value = 4400.00000
		Variable		Value		Reduced Cost
		R		575.00000		0.00000
		C		37.50000		0.00000
		Constraint		Slack/Surplus		Dual Value
		1		0.00000		2.00000
		2		0.00000		10.00000
		3		20.62500		0.00000

		Variable		Objective Coefficient		Allowable Increase		Allowable Decrease
		R		7.00000		8.00000		4.00000
		C		10.00000		13.33330		5.33330
		Constraint		RHS Value		Allowable Increase		Allowable Decrease
		1		700.00000		471.42800		100.00000
		2		300.00000		50.00000		230.00000
		3		100.00000		Infinite		20.62500

1. Determine the objective coefficients ranges. If there is no lower or upper limit, then enter the text "NA" as your answer. Round your answers to two decimal places.

   	Objective Coefficient Range
   Variable	lower limit	upper limit
   Regular Glove	fill in the blank 1	fill in the blank 2
   Catchers Mitt	fill in the blank 3	fill in the blank 4

2. Interpret the ranges in part (a.). As long as the profit per regular glove is between ________________ the optimal solution of ______________ gloves will not change. Or as long as the profit per catcher glove is ______________ the optimal solution of _____________ gloves will not change. The assumption is that ____________ changed at a/the same time.
3. Interpret the right-hand-side ranges. If there is no lower or upper limit, then enter the text "NA" as your answer. Round your answers to two decimal places.

   Constraint	Right-Hand-Side Range
   	lower limit	upper limit
   Cutting and Sewing	fill in the blank 10	fill in the blank 11
   Finishing	fill in the blank 12	fill in the blank 13
   Packaging	fill in the blank 14	fill in the blank 15

   As long as the number of hours available for cutting and sewing (Constraint 1) are _____________ the change in the optimal value of the solution per unit increase in the right-hand side of the constraint is _________ As long as the number of hours available for finishing (Constraint 2) are _____________ the change in the optimal value of the solution per unit increase in the right-hand side of the constraint is ________. As long as the number of hours available for packaging (Constraint 3) are ___________ the change in the optimal value of the solution per unit increase in the right-hand side of the constraint is ____________
4. How much will the value of the optimal solution improve if 20 extra hours of packaging and shipping time are made available? If required, round your answer to three decimal places. Amount: ____________