# Bullseye Shirt Company Problem Assignment

Bullseye Shirt Company makes three types of shirts: Athletic, Varsity, and Surfer. The shirts are made from different combinations of cotton and rayon. The cost per yard of cotton is \$5 and the cost for rayon is \$7. Bullseye can receive up to 4,000 yards of cotton and 3,000 yards of rayon per week.

The table below shows relevant manufacturing information:
Shirt Total Yards of fabric per shirt Fabric requirement Minimum weekly contracts Maximum Demand Selling Price
Athletic 1.00 at least 60% cotton 500 600 \$30
Varsity 1.20 no more than 30% rayon 650 850 \$40
Surfer 0.90 As much as 80% cotton 300 700 \$36

54) Assume that the decision variables are defined as follows:
A = total number of athletic shirts produced
V = total number of varsity shirts produced
S = total number of surfer shirts produced
C = yards of cotton purchased
R = yards of rayon purchased
Xij = yards of fabric i (C or R) blended into shirt J (A, V or S)

Write the objective function.
Answer: max 30 A + 40 V + 36 S – 5C – 7R
Diff: 2 Page Ref: 131-136
Key words: objective function, model construction

55) Write the constraints for the fabric requirements.
Answer: Form of constraints: Total yards used is greater than (or less than) total yards required x (% fabric required) shirts produced
XCA? 0.6 A
XVR ?0.36V
XSC? 0.72 S
Diff: 2 Page Ref: 131-136
Key words: blending

56) Write the constraints for the total number of shirts of each style produced.
Answer: Form of constraint: number of shirts produced = (total yards used to make the shirt)/(yards/shirt)
A =( XCA + XRA)/1
V =( XCV + XRV)/1.2
S =( XCS + XRS)/0.9

Standard form:

A -XCA – XRA) = 0
1.2 V – XCV – XRV =0
0.9 S – XCS – XRS=0

Now we have two question:
first- indicate an appropriate model to formulate the problem and justify your proposed model.
second – Formulate the problem using your proposed model.

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