# Model 10: Detergent Production

The Rosseral Company is a small to medium size detergent manufacturing company. It is one of several companies having production facilities for a new, nonpolluting "washday whitener" which goes by the name of NPW. Rosseral can sell NPW to other detergent manufacturers for \$0.80 per gallon. Rosseral itself manufactures detergent that uses NPW. This NPW can be purchased outside for \$1.20 per gallon (shipping and handling charges have been added) or be obtained from Rosseral's own production. Each gallon of detergent produced requires .1 gallon of NPW. Production costs for NPW and detergent are respectively \$0.50 and \$0.60 per gallon. For the detergent production this cost does not include any cost for the .1 gallon of NPW used in each gallon of detergent. Detergent can be sold for \$0.70 per gallon. Production capacities at Rosseral are: NPW: 10,000 gallons per month; detergent: 120,000 gallons per month. Formulate the problem of maximizing profit as a linear program and solve it.