Chapter 4.5, Problem 32E

Problems 31-36 involve minimization with mixed constraints.

Manufacturing Johnson City Cooperage manufactures 30-gallon and 55-gallon fiber drums. Each 30-gallon drum takes 30 minutes to make, each 55-gallon drum takes 40 minutes to make, and the company has at most 10,000 minutes available each week. Also, workplace limitations and product demand indicate that the number of 55-gallon drums produced plus half the number of 30-gallon drums produced should be at least 160, and the number of 30-gallon drums should be at least twice the number of 55-gallon drums. If Johnson City Cooperages manufacturing costs are $10 for each 30-gallon drum and $15 for each 55-gallon drum, how many of each drum should be made each week to satisfy the constraints at minimum cost? Find the minimum cost.