The famous Australian ski manufacturer Onyx is in the process of finalizing its production program for the Australian winter of 2000. Due to long set-up times, a maximum of four different types of skis are to be produced. In total, there are seven types of skis that can be produced, namely Race Carver (RC), Giant Slalom Ski (RS), Slalom Ski (SL), Cross Carver (CC), Fun Carver (FC), Allround Carver (AC) and Easy Carver (EC). If the RC type is produced, the estimated revenue is 10,400 AUD (Australian dollars, in thousands), for RS it is 8,600 AUD, for SL 7,000 AUD, for CC 3,200 AUD, for FC 3,200 AUD, for AC 12,600 AUD, and for EC 7,300 AUD. The variable production costs (again in thousands of AUD) would be 8,000 for RC, 6,800 for RS, 6,000 for SL, 1,800 for CC, 1,600 for FC, 9,500 for AC, and 6,000 for EC. Furthermore, the following management requirements must be met in the production program:

1) In total, a maximum of 25,000,000 AUD is available to cover variable production costs.

2) To maintain continuity, SL should only be produced if RS is produced.

3) AC should not be produced together with EC.

4) To cover the segment of sporty skiers, at least one type of RC, RS, and SL is to be produced.

5) In addition, the ratio of sporty skis (RC, RS, SL) to all other skis should be at least 1:1.

6) Finally, the ski manufacturer wants to promote beginners and requests that the production of both EC and FC is a prerequisite for the production of SL, and also for the production of CC.

The goal is to maximize the total gross margin (i.e., revenues minus variable production costs) with the help of a linear program.