Assignment:
A company needs to make a plan to produce two products over the period of three months. Table below provides the demand for each product and the total production capacity for each month. The table also provides the production rates (units per hour) for products A and B.
|
Month
|
1
|
2
|
3
|
|
Demand for A (units)
|
500
|
5000
|
750
|
|
Demand for B (units)
|
1000
|
1200
|
1200
|
|
Capacity (hour]
|
3000
|
3600
|
2600
|
|
Production rate (A)
|
1.25
|
1.25
|
1
|
|
Production rate (B)
|
1
|
0.8
|
1.25
|
The company needs to satisfy all the demands. The production system is allowed to produce more and keep some inventory for the next period. However, the holding costs of $0.9 and $0.75 per unit per month are charged for products A and B, respectively. The unit production costs for two products are $30 and $28 for A and B, respectively.
A. Develop the mathematical formulation of this problem.
B. Find the optimal solution. Enough detail and associated computer files should be provided.
C. Suppose that the production manager is allowed to modify the total production capacity for each month. What would be your cost-saving suggestion (based on the sensitivity analysis)? Find the optimal solution.
D. What is the maximum holding cost for product B which does not change the optimal solution you found in part C?
E. Write the associated dual problem for the original model (part A) and find the optimal solution.
F. Comment on the dual (shadow) prices generated in the sensitivity analysis of the dual model.
Provide complete and step by step solution for the question and show calculations and use formulas.