A pharmaceutical manufacturer is considering the production of five possible vaccines. After its initial analysis, the manufacturer must now decide which, and how much, of these vaccines should be produced.

The manufacturer will incur a significant setup cost when starting the production of a vaccine, as shown in the first row of the table below. The table also shows the marginal revenue for each vaccine (per 1,000 units produced), and the manufacturer wants to find the product mix that will maximize its overall profit.

Vaccine 1 2 3 4 5

Setup Cost $85,000 $60,000 $70,000 $40,000 $50,000

Marginal Revenue $75 $80 $90 $60 $70

The manufacturer has two possible locations for the production of these vaccines. It can produce in location A, where 6,000 labor hours are available, or in location B, where 6,500 labor hours are available. The labor requirements (in hours) to produce 1,000 units of each vaccine at each of the locations is given in the following table.

Location 1 2 3 4 5

A 6 4 6 3 5

B 4 5 3 6 4

To retain flexibility, the manufacturer wants to use only one of the locations. The location chosen should be the one that provides the highest profit.

Formulate this problem as a Mixed Integer Programming problem.