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 + 3/2C	900	Cutting and sewing
		1/2R + 1/3C	300	Finishing
		1/8R + 1/4C	100	Packaging and shipping
R, C 0

The sensitivity report is shown in figure below.

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

1. Determine the objective coefficients ranges. Round your answers to two decimal places.

   	Objective Coefficient Range
   Variable	lower limit	upper limit
   Regular Glove
   Catchers Mitt

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 between _________ the optimal solution of _______ gloves will not change. The assumption is that _____ (options only one variable is, both variables are) 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
   Finishing
   Packaging

   As long as the number of hours available for cutting and sewing (Constraint 1) are _____ (above 175, between 175-900, 725 or above, or between 725 and 900) 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 ___ (above 100, 300 or above, between 133.33 and 400, or between 100 and 300) 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 ___(above 100, 25 or above, between 25 and 100, or between 75 and 135) 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?