A machine shop produces steel shafts (S) and steel plates (P) for an automobile manufacturer. The automobile manufacturer requires a minimum of 20 shafts and 20 plates per period. Each shaft contributes $25 of profit and each plate $30 profit.To produce a shaft, the shop estimates that it needs 2 hours of labor and 1 hour of machine time. Each plate requires 3 hours of labor and 1 hour of machine time. The shop has 240 hours of labor and 100 hours of machine time available. The objective is to maximize profit.

Formulate this problem as a linear program, and find the profit-maximizing combination of S and P.