Fedex providing shipping for a major U.S. based company for their new product la
ID: 389720 • Letter: F
Question
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% ofthe 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) Formulate an LP model. List all decision variables, constraints, and write out the full objective function. Week Trucking Limits 45 50 Railway Limits 60 Air Cargo Limits 15 10 45 $140 Costs (S per 1000 tons) $200 $400Explanation / Answer
LP model is following:
Decision variables: Let Xij be the quantity (1000 tons) of cargo assigned to be delivered in week i using mode j of transport where i = 1,2,3 weeks and j = 1,2,3 for Truck, Railway and Air cargo modes.
Objective: Min 200(X11+X12+X13) + 140(X21+X22+X23) + 400(X31+X32+X33)
s.t. Constraints:
X11 <= 45
X12 <= 60
X13 <= 15
X21 <= 50
X22 <= 55
X23 <= 10
X31 <= 55
X32 <= 45
X33 <= 5
X11 + X12 + X13 >= 110000
X21 + X22 + X23 >= 250000*0.7 - 110000
X31 + X32 + X33 = 250000*0.3
All variables >= 0
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