Madras Curry Kitchen offers monthly service plans for providing prepared meals that are delivered to customers’ homes. The target market for these meal plans includes double-income families with no children, and retired couples in upper income brackets. Madras Curry Kitchen offers two monthly plans: Indian Cuisine and Portuguese Cuisine. The Indian Cuisine plan provides frozen meals that are delivered twice each month; this plan generates a contribution margin of $60 for each monthly plan sold. The Portuguese Cuisine plan provides freshly prepared meals delivered on a daily basis; this plan generates a contribution margin of $45 for each monthly plan sold. Madras Curry Kitchen’s reputation provides the company with a market that will purchase all the meals that can be prepared. All meals go through food preparation and cooking steps in the company’s kitchens. After these steps, the Indian Cuisine meals are flash-frozen. The time requirements per monthly meal plan and the hours available per month are as follows: Preparation Cooking Freezing Hours required: Indian Cuisine 2 2 1 Portuguese Cuisine 1 3 0 Hours available 60 120 45 For planning purposes, Madras Curry Kitchen uses linear programming to determine the most profitable number of Indian Cuisine and Portuguese Cuisine monthly meal plans to produce. Required: 1. Using the notation I for Indian Cuisine and P for Portuguese Cuisine, state the objective function and the constraints that Madras Curry Kitchen should use to maximise the total contribution margin generated by the monthly meal plans. 2 marks 2. Graph the constraints on Madras Curry Kitchen’s meal preparation process. Be sure to label the graph clearly, including the optimal solution. 5 marks 3. Using the graph prepared in requirement 2, determine the optimal solution to Madras Curry Kitchen’s production planning problem in terms of the number of each type of meal plan to produce. 2 marks 4. Calculate the value of Madras Curry Kitchen‘s objective function at the optimal solution. (Hint: Contribution margin at the optimal solution). 1 mark
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