# Linear Programming -

Jul 26th, 2015
SoccerBoss
Category:
Mathematics
Price: \$5 USD

Question description

11.  The Two-River Oil company near Pittsburgh transports gasoline to its distributors by truck.  The company has recently contracted to supply gasoline distributors in southern Ohio, and it has \$600,000 available to spend on the necessary expansion of its fleet of gasoline tank trucks.  Three models of gasoline tank trucks are available.

 Truck Model Capacity (Gallons) Purchase Cost Monthly operating cost Super Tanker 5000 67000 550 Regular Line 2500 55000 425 Econo-Tanker 1000 46000 350

The company estimates that the monthly demand for the region will be 550,000 gallons of gasoline.  Because of the size and speed differences of the trucks, the number of deliveries or round trips possible per month of each truck will vary.  Trip capacities are estimated at 15 trips per month for the super tanker, 20 trips per month for the regular line, and 25 trips per month for the Econo-Tanker.  Based on the maintenance and driver availability, the firm does not want to add more than 15 new vehicles to its fleet.  In addition, the company has decided to purchase at least three of the Econo-Tankers for use on short run, low demand routes.  As a final constraint, the company does not want more than half the new models to be super tankers.  The company wishes to satisfy the gasoline demand with minimum monthly operating expense.  Model this problem as a linear programming problem and determine an optimum solution.  Interpret the answers, sensitivity ranges, and shadow prices wherever appropriate.

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