PROBLEM 11 Solutions Plus is an industrial chemicals company that produces specialized cleaning fluids and solvents for a wide variety of applications. Solutions Plus just received an invitation to submit a bid to supply Great North American railroad with a cleaning fluid for locomotives. Great North American needs the cleaning fluid at 11 locations (railway stations); it provided the following information to Solutions Plus regarding the number of gallons of cleaning fluid required at each location: Location Gallons Required Santa Ana El Paso Pendleton Houston Kansas City Los Angeles Glendale Jacksonville Little Rock Bridgeport Sacramento Solutions Plus can produce the cleaning fluid at its Cincinnati plant for $1.20 per gallon. Even though the Cincinnati location is its only plant, Solutions Plus has negotiated with an industrial chemicals company located in Oakland, California, to produce and ship up to 50,000 gallons of the locomotive cleaning fluid to selected Solutions Plus customer locations. The Oakland company will charge Solutions Plus $1.65 per gallon to produce the cleaning fluid, but Solutions Plus thinks that the lower shipping costs from Oakland to some customer locations may offset the added cost to produce the product. The president of Solutions Plus, Charlie Weaver, contacted several trucking companies to negotiate shipping rates between the two production facilities (Cincinnati and Oakland) and the locations where the railroad locomotives are cleaned. The quotes received in terms of dollars per gallon are shown below. Note that the "-" entries identify shipping routes that will not be considered because of the large distances involved. These quotes for shipping rates are guaranteed for one year. Cincinnati Oakland Santa Ana El Paso Pendleton Houston Kansas City Los Angeles Glendale` Jacksonville Little Rock Bridgeport Sacramento 22,418 6,800 80,290 100,447 241,570 64,761 33,689 68,486 148,586 111,475 112,000 0.84 0.83 0.45 0.36 0.34 0.34 0.34 0.22 0.74 0.49 0.22 0.22 0.15 To submit a bid to the railroad company, Solutions Plus must determine the price per gallon they will charge. Solutions Plus usually sells its cleaning fluids for 15% more than its cost to produce and deliver the product. For this big contract, however, Fred Roedel, the director of marketing, suggested that maybe the company should consider a smaller profit margin. In addition, to ensure that if Solutions Plus wins the bid, they will have adequate capacity to satisfy existing orders as well as accept orders for other new business, the management team decided to limit the number of gallons of the locomotive cleaning fluid produced in the Cincinnati plant to 500,000 gallons at most.