Red Brand-Case Solusion Essay

929 Words4 Pages
Information： Amount of incoming tomatoes: 3,000,000 pounds Grade A：20%×3,000,000 = 600,000 pounds Grade B：80%×3,000,000 = 2,400,000 pounds Product Selling Price Per Case Demand Forecast (Cases)(1) Pounds Per Case(2) Total weight in pounds(1)*(2)
Minimum Quality requirement

Whole tomatoes \$4.00 800,000 18 14,400,000
8 \$1.48

Tomato juice \$4.50 50,000 20 1,000,000
6 \$1.32

Tomato paste \$3.80 80,000 25 2,000,000
5 \$1.85

Contribution per case (3) Contribution per pound (excl Tomato cost) (3)/(2)

\$0.082

\$0.066

\$0.074

WA = Pounds of A-grade tomatoes in canned whole tomatoes.. WB = Pounds of B-grade tomatoes in canned whole tomatoes. JA = Pounds of A-grade tomatoes in tomato juice. JB = Pounds of B-grade tomatoes in
Disregard Mitchell Gordon's idea of purchasing additional tomatoes. Define the decision variables in terms of pounds of tomatoes. Objective function: Max Z =0.0822(WA+WB)+0.066(JA+JB)+0.074(PA+PB)- 180,000 Constraints: WA+JA+PA≤600,000 WB+JB+PB≤2,400,000 WA+WB≤14,400,000 JA+JB≤1,000,000

PA+PB≤2,000,000 (9WA+5WB)/ (WA+WB)≥ 8 =>WA≥3WB (9JA+5JB)/ (JA+JB) ≥6 WA, JA, PA, WB, JB, PB≥0 Q3： Solve your model and interpret the solution decision variables contribution
WA 525,000 0.082 WB 175,000 0.082 JA 75,000 0.066 JB PA 225,000 0 0.066 0.074 PB 2,000,000 0.074 Objective 45355.5556

=> WA-3WB≥0

=> 3JA≥JB

=> 3JA-JB≥0

Product Grade A Tomato（pounds） Grade B Tomato（pounds） Total Tomatoes（pounds） Pounds per case Total cases Q4：

Whole tomatoes
525,000 175,000 700,000 18 38888.8889

Tomato juice
75,000 225,000 300,000 20 15000

Tomato paste
0 2,000,000 2,000,000 25 80000

In an optimal solution, when the shadow price value of a constraint is 0, it means that the variable has a positive slack/surplus, the allowable increase is 600,000, more than 80,000, and thus all the additional 80,000 pounds of tomatoes should be purchased.

Q5：

Add Constraints: WP = Pounds purchased into canned whole tomatoes JP= Pounds purchased into tomato juice PP= Pounds purchased into tomato pasta 0.0822-0.085=-0.0028 0.066-0.085=-0.019