Kelson Sporting Equipment, Inc., makes two different types of baseball gloves: a regular model and a catcher's model. Letting

R = number of regular gloves

C = number of catcher's mitts

leads to the following formulation:

Max	6R	+	9C
s.t.
	R	+	3 2 C		800	Cutting and sewing
	1 2 R	+	1 3 C		300	Finishing
	1 8 R	+	1 4 C		100	Packaging and shipping
	R,	C	0

The sensitivity report is shown below.

Variable Cells

Model Variable	Name	Final Value	Reduced Cost	Objective Coefficient	Allowable Increase	Allowable Decrease
R	Gloves Standard	500.000	0.000	6.000	7.500	1.500
C	Gloves Deluxe	150.000	0.000	9.000	3.000	5.000

Constraints

Constraint Number	Name	Final Value	Shadow Price	Constraint R.H. Side	Allowable Increase	Allowable Decrease
1	Cutting and Dyeing Hours Used	725.000	0.000	800.000	1E+30	75.000
2	Finishing Hours Used	300.000	4.500	300.000	100.000	166.667
3	Packaging and Shipping Hours Used	100.000	30.000	100.000	15.000	25.000

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

regular glove _____

catcher's mitt _____

value _____

(b) Which constraints are binding? (Select all that apply.)

cutting and sewing

finishing

packaging and shipping

(c) What are the shadow prices for the resources? Interpret each.

constraint 1

Each additional hour of cutting and sewing will improve profits by $30.00.

Each additional hour of cutting and sewing will improve profits by $75.00.

Each additional hour of cutting and sewing will improve profits by $4.50.

Additional hours of cutting and sewing will not improve profits.

constraint 2

Each additional hour of finishing will improve profits by $30.00.

Each additional hour of finishing will improve profits by $75.00.

Each additional hour of finishing will improve profits by $4.50.

Additional hours of finishing will not improve profits.

constraint 3

Each additional hour of packing and shipping will improve profits by $30.00.

Each additional hour of packing and shipping will improve profits by $75.00.

Each additional hour of packing and shipping will improve profits by $4.50.

Additional hours of packing and shipping will not improve profits.

(d) If overtime can be scheduled in one of the departments, where would you recommend doing so?

cutting and sewing

finishing

packaging and shipping