The BigRig Trucking Company participates in an Internet transportation exchange where customers advertise their shipments including load weight and volume, and trip origin and destination. BigRig then computes the cost and time of the trip and determines the bid it should make for the shipment to achieve a certain profit level. Twelve customers have posted shipments on the exchange, and BigRig has three trucks available for shipments. Each truck has a load capacity of 80,000 pounds and 5,500 cubic feet and available driving time of 90 hours. The following table shows the load parameters (i.e., weight in pounds and volume in cubic feet) for each customer shipment and the profit BigRig would realize from each shipment:

Formulate and solve a linear programming model to determine which customer shipments BigRig should bid on in order to maximizeprofit.

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Customer Profit (S) Load (lb) Load (ft) Time (hours) 1,600 17,000 39,000 2,100 15,000 24,000 3.200 7,000 33,000 3.700 18,000 18,000 4400 12,000 21,000 2,900 1.100 1,600 800 6,200 36,000 1,800 14,000 55,000 3.700 2,900 20,000 44,000 51 45 36 110 105 5,000 4,600 11,000 23,000 15,000 19,000 56 10 37 41 12 9,000 45,000