Chapter 4.5, Problem 31E

Problems 31-36 involve minimization with mixed constraints.

Water purification Nolan Industries manufactures water filters/purifiers that attach to a kitchen faucet. Each purifier consists of a housing unit that attaches to the faucet and a 60-day filter (sold separately) that is inserted into the housing. Past records indicate that on average, the number of filters produced per week should be at least 400. It takes 20 minutes to make and assemble each filter and 40 minutes for each housing. The manufacturing facility has at least 20,000 minutes per week for making and assembling these units, but due to certain parts supply constraints, the number of housing units per week can be at most 400. If manufacturing costs (for material and labor) are $6.60 for each filter and $8.35 for each housing unit, how many of each should be produced to minimize weekly costs? Find the minimum cost.