The Suitcase Manufacturing Company produces a number of different types of suitcases of varying qualities, which are called S1, S2, S3, S4 and S5. The manufacturing process involves different departments in the factory, and we call these departments D1 to D6. Each suitcase requires time (in minutes) in the various departments as follows

D1 D2 D3 D4 D5 D6

S1 10 15 10 12 5 5

S2 15 20 16 20 5 5

S3 21 25 20 20 8 8

S4 26 21 28 25 10 10

S5 33 28 30 29 15 15

The contribution of gross profit (i.e., the selling price less the cost of raw materialls) of each type

of suitcase is given in the following table, which also shows the minimum number of each type

of suitcase that must be produced together with the maximum number (in terms of contracts with

retail stores)

S1 S2 S3 S4 S5

Profit (Rands) 120 150 235 300 350

Minimum number 200 100 100 100 100

Maximum number 500 300 300 300 300

In addition, there is, this month, a supply limitation on the locks used on the higher quality suitcases

(S3, S4 and S5), and the total production of these suitcases cannot exceed 600.

Each department can provide 24000 minutes per month, except Department D6, which can only offer 15000 minutes. How much of each product line should be produced so as to maximize the company’s trading profit?