Great Cooking Company 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.

Great Cooking 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; this plan generates a contribution margin of $45 for each monthly plan sold.

Great Cooking'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 premier cuisine meals are flash-frozen. The time requirements per monthly meal plan and the hours available per month are as follows:

House Require

premier cuisine

1. Preparation 2
2. cooking 2
3. Freezing 1

Haute cuisine

1. Preparation 1
2. Cooking 3
3. Freezign 0

Hours Available

1. Preparation 60
2. Cooking 120
3. Freezing 45

For planning purposes, Great Cooking 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 Great Cooking should use to maximise the total contribution margin generated by the monthly meal plans.
2. Graph the constraints on Great Cooking's meal preparation process. Be sure to label the graph clearly, including the optimal solution.
3. Using the graph prepared in requirement 2, determine the optimal solution to Great Cooking's production planning problem in terms of the number of each type of meal plan to produce.
4. Calculate the value of Great Cooking's objective function at the optimal solution.
5. If the constraint on preparation time could be eliminated, determine the revised optimal solution.