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	+	7C
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 computer solution is shown below.

Optimal Objective Value = 4050.00000

Variable	Value	Reduced Cost
R	500.00000	0.00000
C	150.00000	0.00000

Constraint	Slack/Surplus	Dual Value
1	75.00000	0.00000
2	0.00000	7.50000
3	0.00000	18.00000

Variable	Objective Coefficient	Allowable Increase	Allowable Decrease
R	6.00000	4.50000	2.50000
C	7.00000	5.00000	3.00000

Constraint	RHS Value	Allowable Increase	Allowable Decrease
1	800.00000	Infinite	75.00000
2	300.00000	100.00000	166.66667
3	100.00000	15.00000	25.00000

(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 dual values for the resources? Interpret each.

constraint 1

Each additional hour of cutting and sewing will improve profits by $18.00.

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

Each additional hour of cutting and sewing will improve profits by $7.50.

Additional hours of cutting and sewing will not improve profits.

constraint 2

Each additional hour of finishing will improve profits by $18.00.

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

Each additional hour of finishing will improve profits by $7.50.

Additional hours of finishing will not improve profits.

constraint 3

Each additional hour of packing and shipping will improve profits by $18.00.

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

Each additional hour of packing and shipping will improve profits by $7.50.

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