### 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)