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
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.