Kelson Sporting Equipment Inc makes two different types of b

Kelson Sporting Equipment, Inc., makes two different types of baseball gloves: a regular 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:

Solution

Given information :

Kelson sporting equipment :

Hrs available

Cutting 200

Sewing 300

Packaging 100

We will formulate the table as per the given information.

Let X1 be the variable for Regular model

X 2 be the variable for Calchers model .

Now as per the data mentioned on table we can formulate the equation.

Let Z objective function .Here profit has been mentioned so we have to maximize this equation.

Objective equation

Z Maximize = 5X1 + 8X2

subject to

Constraint equation

X1 + 1.5 X2 </= 200 (Cutting & Sewing Eqn)

0.5 X1 + 0.33 X2 </= 300 (Finishing Eqn)

0.125 X 1 + 0.25 X2 < / = 100   (Packaging & Shipping )

Where X1 & X2 > 0

Now we have to solve this equation ,

We will solve this problem by simplex method

Tableau #1
x1 x2 s1 s2 s3 z   
1 1.5 1 0 0 0 200
0.5 0.33 0 1 0 0 300
0.125 0.25 0 0 1 0 100
-5 -8 0 0 0 1 0

Tableau #2
x1 x2 s1 s2 s3 z   
0.666667 1 0.666667 0 0 0 133.333
0.28 0 -0.22 1 0 0 256
-0.0416667 0 -0.166667 0 1 0 66.6667
0.333333 0 5.33333 0 0 1 1066.67

Optimal Solution: z = 1066.67; x1 = 0, x2 = 133.333

c) Total Profit earn by kelson

Z = $ 1066.67

d)

Scheduled production in each department

d )

Slack time in each department

Cutting = 200 - 200 = 0

Finishing = 300 - 44 = 265

Packaging = 100 - 33 = 67

	Cutting &Sewing	Finishing	Packaging & Shipping	Profit
Model
Regular	1	0.5	0.125	$5
Calcher	1.5	0.33	0.25	$8
Hrs Available	200	300	100