Time Saver Meals, Inc., offers monthly service plans providing prepared meals that are delivered to the customers€™ homes. The target market for these meal plans includes double-income families with no children and retired couples in upper income brackets. The firm offers two monthly plans: Premier Cuisine and Haute Cuisine. The Premier 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 Haute Cuisine plan provides freshly prepared meals delivered on a daily basis and generates a contribution margin of $45 for each monthly plan sold. The company€™s reputation provides 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 Premier Cuisine meals are flash frozen. The time requirements per monthly meal plan and hours available per month are as follows:

For planning purposes, management uses linear programming to determine the most profitable number of Premier Cuisine and Haute Cuisine monthly meal plans to produce.

Required:
1. Using the notation P for Premier Cuisine and H for Haute Cuisine, state the objective function and the constraints that management should use to maximize the total contribution margin generated by the monthly meal plans.
2. Graph the constraints on the meal preparation process. Be sure to clearly label the graph.
3. Using the graph prepared in requirement (2), determine the optimal solution to the company€™s production planning problem in terms of the number of each type of meal plan to produce.
4. Calculate the value of the objective function at the optimal solution.
5. If the constraint on preparation time could be eliminated, determine the revised optimal solution.
(CMA,adapted)

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Preparation Cooking Freezing Hours required: Premier Cuisine Haute Cuisine Hours available 60 120 45