Red Brand-Case Solusion Essay

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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…show more content…
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

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