Problem

A plumbing manufacturer makes two lines of bathtubs, model A and model B. Every tub requires blending a certain amount of steel and zinc; the company has available a total of 24,500 pounds of steel and 6,000 pounds of zinc. Each model A bathtub requires a mixture of 120 pounds of steel and 20 pounds of zinc, and each yields a profit of $90. Each model B tub produced can be sold for a profit of $70; it requires 100 pounds of steel and 30 pounds of zinc. To maintain an adequate supply of both models, the manufacturer would like the number of model A tubs made to be no more than 5 times the number of model B tubs. Find the best product mix of bathtubs.