### What is the optimal production schedule for this firm

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##### Reference no: EM131027452

Question 1-

 Activity Mean duration Std. dev. (days) A 11 0.9 B 13 1.1 C 7 0.2 D 9 0.8 E 6 1 F 7 1.2 G 10 0.7 H 9 0.6 I 8 0.8

Table 1

Complete the following:

1. Calculate the project completion time.

2. Indicate the critical path activities.

3. What is the probability of completing this project between 38 and 40 days?

4. What are the slack values for activities C and F? Interpret the meaning of their slack values?

Question 2 - A registered nurse is trying to develop a diet plan for patients. The required nutritional elements are the total daily requirements of each nutritional element as indicated in Table 2:

Required nutritional element total and daily requirements

 Calories Not more than 2,700 calories Carbohydrates Not more than 300 grams Protein Not less than 250 grams Vitamins Not less than 60 units

Table 2

The nurse has four basic types to use when planning the menus. The units of nutritional element per unit of food type are shown in Table 3 below. Note that the cost associated with a unit of ingredient also appears at the bottom of Table 3.

Required nutritional element and units of nutritional elements per unit of food type

 Element Milk Chicken Bread Vegetables Calories 160 210 120 150 Carbohydrates 110 130 110 120 Protein 90 190 90 130 Vitamins 50 50 75 70 Cost per unit £0.42 £0.68 £0.32 £0.17

Table 3

Moreover, due to dietary restrictions, the following aspects should also be considered when developing the diet plan:

1. The chicken food type should contribute at most 25% of the total caloric intake that will result from the diet plan.

2. The vegetable food type should provide at least 30% of the minimum daily requirements for vitamins.

Complete the following: Provide a linear programming formulation for the above case. (You do not need to solve the problem.)

Individual Project-

The purpose of this simulation project is to provide you with an opportunity to use the POM-QM for Windows software to solve a linear programming problem and perform sensitivity analysis.

POM-QM for Windows software

For this part of this project, you will need to use the POM software:

1. Read Appendix IV of the Operations Management (Heizer & Render, 2011) textbook.

2. Install and launch the POM-QM for Windows software and from the main menu selectModule, and then Linear Programming.

3. Program the linear programming formulation for the problem below and solve it with the use of POM. (Refer to Appendix IV from the Heizer and Render (2011) textbook.)

For additional support, please reference the POM-QM for Windows manual provided in this week's Learning Resources.

Individual Project problem

A firm uses three machines in the manufacturing of three products:

• Each unit of product 1 requires three hours on machine 1, two hours on machine 2 and one hour on machine 3.
• Each unit of product 2 requires four hours on machine 1, one hour on machine 2 and three hours on machine 3.
• Each unit of product 3 requires two hours on machine 1, two hours on machine 2 and two hours on machine 3.

The contribution margin of the three products is £30, £40 and £35 per unit, respectively.

Available for scheduling are:

• 90 hours of machine 1 time;
• 54 hours of machine 2 time; and
• 93 hours of machine 3 time.

The linear programming formulation of this problem is as follows:

Maximise Z = 30X1 + 40X2 + 35X3

3X1 + 4X2 + 2X3 <= 90

2X1 + 1X2 + 2X3 <= 54

X1 + 3X2 + 2X3 <= 93

With X1, X2, X3 >= 0

1. What is the optimal production schedule for this firm? What is the profit contribution of each of these products?

2. What is the marginal value of an additional hour of time on machine 1? Over what range of time is this marginal value valid?

3. What is the opportunity cost associated with product 1? What interpretation should be given to this opportunity cost?

4. How many hours are used for machine 3 with the optimal solution?

5. How much can the contribution margin for product 2 change before the current optimal solution is no longer optimal?

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