Question

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 200 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	3/2	1/6	$4
Catcher's model	3/2	1/2	1/2	$8

Assuming that the company is interested in maximizing the total profit contribution, answer the following:

(a)	What is the linear programming model for this problem? If required, round your answers to 3 decimal places or enter your answers as a fraction. If the constant is "1" it must be entered in the box. Do not round intermediate calculation. If an amount is zero, enter "0"
	Let R = number of units of regular model. C = number of units of catcher's model.
	Max R + C s.t. R + C .    - Select your answer -≤≥= ____ Cutting and Sewing R + C - Select your answer -≤≥=____ Finishing R + C - Select your answer -≤≥=_____ Packing and Shipping R, C - Select your answer -≤≥=______
(b)	Develop a spreadsheet model and find the optimal solution using Solver. How many gloves of each model should Kelson manufacture? If your answer is zero enter “0”.
	Regular Model = ____ units
	Catcher's Model =_____ units
(c)	What is the total profit contribution Kelson can earn with the given production quantities?
	$
(d)	How many hours of production time will be scheduled in each department?
	Department Time Used (Hours) Cutting and Sewing Finishing Packing and Shipping
(e)	What is the slack time in each department? If your answer is zero, enter “0”.
	Department Slack Time (Hours) Cutting and Sewing Finishing Packing and Shipping

Answer 1

Let

R = number of units of regular model.
C   = number of units of catcher's model.

these are the decision variables

The profit from making R units of regular gloves is $4R and the profit from making C units of catcher's model is $8C

The total profit is

We want to maximize this and it is the objective function.

Next the constraints

700 hours of production time available in its cutting and sewing department. the total cutting and sewing hours required to produce a quantity of R and C cannot be more than 700

• 

300 hours of production time available in finishing department. the total finishing hours required to produce a quantity of R and C cannot be more than 300

• 

200 hours of production time available in packing and shipping department. the total packing and shipping hours required to produce a quantity of R and C cannot be more than 200

• 

a) The LP model is

Max	4R	+	8C
s.t.
	1R	+	3/2C .	<= 700	Cutting and Sewing
	3/2R	+	1/2C	<= 300	Finishing
	1/6R	+	1/2C	<= 200	Packing and Shipping
			R, C	>=0

b) Prepare the following sheet

get this

set up the solver using data--->solver

get the following

b) How many gloves of each model should Kelson manufacture?

Regular Model = 75 units
Catcher's Model = 375 units

c) What is the total profit contribution Kelson can earn with the given production quantities?

ans: $3,300

d) How many hours of production time will be scheduled in each department?

We use the following

to get

ans:

Department	Time Used (Hours)
Cutting and Sewing	637 1/2
Finishing	300
Packing and Shipping	200

e) What is the slack time in each department?

We subtract the above from the available capacity to get the slack

Department	Time Used (Hours)	Time available (Hours)	slack time (available - used)
Cutting and Sewing	637 1/2	700	62 1/2
Finishing	300	300	0
Packing and Shipping	200	200	0