Linear Programming -

11.The Two-River Oil company near Pittsburgh transports gasoline to itsdistributors by truck. The company hasrecently contracted to supply gasoline distributors in southern Ohio, and ithas $600,000 available to spend on the necessary expansion of its fleet ofgasoline tank trucks. Three models ofgasoline tank trucks are available.TruckModelCapacity (Gallons)Purchase CostMonthly operatingcostSuperTanker500067000550RegularLine250055000425Econo-Tanker100046000350The company estimates that themonthly demand for the region will be 550,000 gallons of gasoline. Because of the size and speed differences ofthe trucks, the number of deliveries or round trips possible per month of eachtruck will vary. Trip capacities are estimatedat 15 trips per month for the super tanker, 20 trips per month for the regularline, and 25 trips per month for the Econo-Tanker. Based on the maintenance and driveravailability, the firm does not want to add more than 15 new vehicles to itsfleet. In addition, the company hasdecided to purchase at least three of the Econo-Tankers for use on short run,low demand routes. As a finalconstraint, the company does not want more than half the new models to be supertankers. The company wishes to satisfythe gasoline demand with minimum monthly operating expense. Model this problem as a linear programmingproblem and determine an optimum solution.Interpret the answers, sensitivity ranges, and shadow prices whereverappropriate.