2. Four products are processed sequentially on three machines in an aircraft maintenance

workshop. The following Table 1 gives the operational data of the problem.

Machine

1

2

3

Unit selling price ($)

Table 1: Operational data for the problem

Manufacturing time (hr) per unit

Cost per hr Product Product Product Product Capacity

$

2

3

4

(hr)

10

3

4

2

500

5

2

1

2

380

4

3

2

1

450

70

55

45

2375

(a) Formulate the problem as a Linear Programming (LP) problem (30 marks).

(b) Determine the optimal product-mix in the production schedule and the optimal profit

using the simplex approach (50 marks)