Question

Can somebody please formulate this as a Linear programming problem

The Consolidated Company has in the past contracted out the shipment of its products from its factory to its warehouses. The volume of deliveries is measured in ton- miles (the tons of product times the number of miles over which it is to be delivered.) Consolidated has 400000 ton- miles to be delivered each month. Currently, the Company engages the services of Speedy Trucking Co. and paying at the rate of 0.5 $ per ton- mile to deliver the product. Consolidated is considering the purchase of a fleet of trucks to take over a part or all of this delivery service.
Three types of trucks are under consideration – large trailer trucks, medium- size trucks and pick- up trucks. The details of capacity and costs are given below:

Type of truck - Large trailer- trucks, Medium- size trucks and Pick- up trucks
Purchase Cost ($) - 15000(large trailer trucks), 8000(medium size trucks) and 5000(pick-up trucks).
Operating cost per ton-mile($) - 0.28(large trailer trucks), 0.32(medium size trucks) and 0.40(pick up trucks)
Capaity ton-miles per month - 10000(large trailer trucks), 8000(medium size trucks) and 6000(pick up trucks)

Speedy Trucking has indicated that it would be willing to deliver any excess not delivered by Consolidated’s own trucks at the same rate of 50 cents per ton- mile.
Capital equipment funds are in short supply in Consolidated, and only $ 380000 is available for the investment. In addition to the budget limitation, there are other restrictions on the types of trucks purchased. The first involves dock loading space. Because of parking space and dock imitations, not more than 28 truck spaces are available. A trailer or medium-size truck would use one space. Two pick-up trucks use one space. Also, because of the types and size of deliveries, at least two thirds of the trucks purchased would have to be either trailers or medium- size trucks.

Answer 1

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