Contribution per case (3) Contribution per pound (excl Tomato cost) (3)/(2)
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
Product Grade A Tomato（pounds） Grade B Tomato（pounds） Total Tomatoes（pounds） Pounds per case Total cases Q4：
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.
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