Red Canners needs to optimize its product mix to maximize profits given constraints around demand, available tomatoes, and product quality. The objective is to maximize profits calculated from revenues of different products minus $180,000 in fixed costs. Constraints include limits on demand for each product, total tomatoes available which are split between higher quality Grade A and Grade B, and minimum quality thresholds for products. The solution provides the optimal product mix that generates the maximum profit while satisfying all constraints. It is determined that buying additional Grade A tomatoes would increase profits.

1. RED BRAND CANNERS QM Case

2. Case Overview

3. Description of Objectives & Constraints To calculate optimized product mix of Red Canners products to maximize profit.!! Constraints – Demand Constraint Availability Constraint Quality Constraint & Whether to buy more Grade A Tomatoes.??

4. 4 Input & Output Variables

5. 5 Variables in Decision Making

6. 6 Objective Function Maximize Profit: 1.48 X (AC+BC) / 18 + 1.32 X (AJ + BJ) / 20 + 1.85 X (AP+BP) / 25 – 180,000. OR MAX. 0.0822AC + 0.0822BC + 0.066AJ + 0.066BJ + 0.740AP + 0.740BP – 180,000.

7. 7 Subjected to: Demand Constraint (from exhibit – 1) Constraints- AC + BC ≤ 14,400,000. AJ + BJ ≤ 1,000,000. AP + BP ≤ 2,000,000.

8. 8 Subjected to: Availability Constraint Total tomatoes available = 3,000,000 pounds Grade A = 600,000. Grade B = 2,400,000. Constraints- AC + AJ + AP ≤ 600,000. BC + BJ + BP ≤ 2,400,000.

9. 9 Subjected to: Quality Constraint Constraints(Weighted avg. method)- AC – 3BC ≥ 0. 3AJ – BJ ≥ 0. BP ≥ 0.

10. 10 Solution No since Fixed cost increases by 0.75million and revenue increases by only 0.7million

11. 11 Optimum Sloution

12. We can further consume 600,000 pounds of Grade A Tomatoes. Increase in revenue by .0903 cents per pound. 12 We should buy more.?

13. 13 THANK YOU