### A department has three machines available, and the new department

The J. Mehta Company’s production manager is planning a series of one-month production periods for stainless steel sinks. The forecasted demand for the next four months is as follows:

 Month Demand for Stainless Steel Sinks 1 120 2 160 3 240 4 100

The Mehta firm can normally produce 100 stainless steel sinks in a month. This is done during regular production hours at a cost of \$100 per sink. If demand in any one month cannot be satisfied by regular production, the production manager has three other choices:

(1) he can produce up to 50 more sinks per month in overtime but at a cost of \$130 per sink;

(2) he can purchase a limited number of sinks from a friendly competitor for resale (the maximum number of outside purchases over the four-month period is 450 sinks, at a cost of \$150 each);

(3) Or, he can fill the demand from his on-hand inventory (i.e. beginning inventory). The inventory carrying cost is \$10 per sink per month (i.e. the cost of holding a sink in inventory at the end of the month is \$10 per sink).

A constant workforce level is expected. Back orders are NOT permitted (e.g. order taken in period 3 to satisfy the demand in later period 2 is not permitted). Inventory on hand at the beginning of month 1 is 40 sinks (i.e. beginning inventory in month 1 is 40 sinks)

a. Set up and formulate algebraically the above “production scheduling” problem asa TRANSPORTATION Model to minimize cost. (16 points)

b. SOLVE using Excel solver (Provide a printout of the corresponding “Excel Spreadsheet” and the “Answer Report”). Also include a managerial statement that describes verbally the results. (10 points)

Note: This problem can be formulated as multi-period production scheduling LP problem.However, if you try to formulate it this way then you will get ZERO as the problem requirement is to formulate it as a transportation problem.

Problem 2 (21 points)

A department has three machines available, and the new department manager must select one of the machines to assign to a new product line. The product line will consist of three slightly different products, A, B and C. Production requirements, machine capacities and setup costs are given in the following table:

 Machine Setup Cost Production time per pound Capacity (hours) A                     B                   C 1 \$150 4                    3                   5 1000 2 \$120 3                   2                    4 800 3 \$110 2                   4                   2 700

The revenue per pound on the three products is listed in the following table:

 Product Revenue A \$13 B \$10 C \$12

a. Formulate algebraically this problem that will maximize the net profit taking into account an additional factor: At least 40 pounds of each product must be made. (14 points)

b. Solve for the optimal solution and profit using Excel solver (Provide a printout of the corresponding “Excel Spreadsheet” and the “Answer Report”). Also include a managerial statement that describes verbally the results. (7 points)

Problem 3 (23 points)

California Tours is planning a group bus trip that for the following candidate cities in the table below. Also included are the total costs for the group to visit those cities on the tour.

 City Cost(\$) San Fransisco (SF) 5000 Oakland (OK) 4500 Palo Alta (PA) 3600 San Jose (SJ) 4100 San Mateo (SM) 3500 Concord (CO) 2500 Santa Cruz (SC) 3200 Monterey (MN) 4000

To plan the trip, three prioritized goals are listed below, in order of importance.

P1: Avoid spending more than \$15000 for the total trip.

P2: Visit at least 5 cities.

P3: Include San Mateo in the tour.

a. Formulate a goal programming model that will help to determine the number of cities to include in the tour. (14 points)

b. Find the optimal solution using Solver. (Provide a printout of the Answer report and theExcel spreadsheet formulation). Also include a managerial statement that describes verbally the results. (9 points)