Fedex providing shipping for a major U.S. based company for their new product launch. Their contract calls for a total of 250,000 tons of material to be delivered over a three-week period. Fedex can use multi modes of transportation: trucks, railroads, and air cargo. Their contract requires 110,000 tons delivered by the end of week one, 70% of the total delivered by the end of week two, and the entire amount delivered by the end of week three. Contracts in place with the transportation companies call for at least 45% of the total delivered be delivered by trucking, at least 40% of the total delivered be delivered by railway, and up to 15% of the total delivered be delivered by air cargo. Unfortunately, competing demands limit the availability of each mode of transportation each of the three weeks to the following levels (all in thousands of tons):
Week Trucking Limits Railway Limits Air Cargo Limits
1 45 60 15 2 50 55 10 3 55 45 5
Costs ($ per 1000 tons) $200 $140 $400
a. Formulate an LP model. b. Solve it using Excel solver