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:

1) 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

Main Heading: A Blend Example

Key words: objective function, model construction

2) 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

Main Heading: A Blend Example

Key words: blending

3) 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.