Problem 1
Consider the Reddy Mix problem
(a) Implement and solve this optimization problem using Excel Solver.
(b) Produce the sensitivity reports and explain meaning of each column in the report
(c) Introduce a new product ("ecopaint") into the problem that requires 2 units of raw material Ml and 1 unit of raw material M2. Other constraints are not affected. What should be the minimal price of the new product at which it is profitable to produce non-zero quantity of it?
Hint: Start with 0 price
(d) Explain how the shadow prices, dual prices and reduced costs are related using the results from parts a,b and c.
Problem 2
Acme Manufacturing Company has received a contract to deliver home windows over the next 6 months. The successive demands for the 6 periods are 100, 250, 190, 140, 220, and 110 units, respectively. Production cost per window varies from month to month depending on the cost of labor, material, and utilities. Acme estimates the production cost per window over the next 6 months to be $50, $45, $55, $48, $52, and $50, respectively. To take advantage of the fluctuations in manufacturing cost, Acme may elect to produce more than is needed in a given month and hold the excess units for delivery in later months. This, however, will incur storage costs at the rate of SS per window per month assessed on end-of-month inventory.
(a) Formulate the LP problem to determine the optimum production schedule that minimizes the total costs.
(b) Implement and solve this optimization problem using Excel Solver
(c) Assuming that one employee can produce 10 windows a month. What will be the minimal number of employees required in each month.
(d) Assuming that each employee must get one month vacation after 5 consec¬utive working month, and each employee gets $15000 for the half year period. Add necessary variables and constraints to the initial problem and decide how many employees should work in the company (still minimizing the total costs).
Problem 3
A manufacturing company has a production plan where they produce 21 unit every week for the next 50 weeks. However, the demands and related costs (production and inventory) are fluctuating from week to week due to some external factors. Therefore, some overproduction and high inventory costs are encountered.
The demands, costs and the current production plan can be found in the attached excel file. Formulate the optimization problem and re-optimize the production plan.