QUESTION 1(15 marks) A company is trying to determine which of its four factories should produce a certain product. For each factory, the fixed setup cost, the labour hours needed to produce one unit, and the total labour hours available at the factory are given in the following table:

If a factory does not produce the product, then the fixed setup cost is zero. If a factory produces the product, then the fixed setup cost remains the same for any number of units. The cost of each labour hour is $1. As an example, if factory 1 produces 100 units, its cost will be 3000+100?4 = 3400 dollars.

The product should be shipped to two customers. Customer 1 needs 400 units. Customer 2 needs 600 units. The cost of shipping one unit from each factory to each customer is given in the following table:

The production plan needs to satisfy the following requirements:

• Each customer must get the product from at least two factories.

• If customer?i?gets the product from factory?j, the number of units shipped from factory j to customer i must be at least 50 units.

Formulate a mixed integer linear programming model whose solution will tell the company how to meet the demand at minimal cost.

Making Criteria:

• Clear definition of all decision variables

• Clear explanation and correct formulation for objective function

• Clear explanation and correct formulation for each constraint?

• Correct variable domains?

factory Factory 1 Factory 2 Factory 3 Factory 4 fixed setup cost $3,000 $4,000 $6,000 $5,000 labour hours per unit 4 2 1 3 labour hours available 952 574 521 695 Factory 1 Factory 2 Factory 3 Factory 4 Customer 1 $2 $5 $3 $8 Customer 2 $7 $6 $3 $1