Question

2. A company that manufactures compressors has plants in three locations: Cleveland, Chicago, and Boston. During a week, the total capacity of each plant to produce one type of special compressor is 25, 45, and 35 units, respectively. The company wants to ship at least 40, 10, 20 and 30 units to distribution centers in Dallas, Atlanta, San Francisco, and Philadelphia respectively. The unit production and distribution costs from each plant to each distribution center are given in the table below. How many of these compressors should be shipped from each manufacturing plant to each distribution center, if the company's goal is to minimize the total cost? (24pts) Table: Unit production and shipping costs, availability of compressors, and demand for compressor units Distribution centers an Plants Dallas Atlanta FranciscoPhiladelphia |Availabilit Cleveland 2 2 4 10 25 45 35 4 са 2 10 20 Boston Requirements 40 30

Answer 1

Since the availability is more than the requirements, we will need to add a dummy distribution center

Let us put these values in solver -

The objective function in green cell has to be minimized by changing the values in blue cells.

The constraints are applied on total requirement and total availability.

Let us initially assume the requirement at each center to be 1. The solver will optimize this requirement to find the minimum cost.

Run the solver to get -

Hence, the number of compressors shipped from manufacturing plants to distribution centers are -