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LP, Operation Management

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SHAYO & Sons is a canning company in Arusha that currently operates two small canning State Mining Corporation (SMC) is establishing a production plan for the current week at its Mwanza code, which has three main veins of varying characteristics. The net yield per ton for each of the veins is provided in the table below:

ORE MINING VEINS
Eastern Northern Central
Gold 0.2 gm 0.3gm 0.4gm
Silver 30gm 20gm 30gm
Copper 50kg 20kg 25kg

Gold presently sold for shs. 9000 per gram. Silver sells for shs. 450 per gram and copper sells for shs. 300 per kilogram. The eastern vein is the most accessible one, requiring only 1 man hour per ton of ore. The northern and central veins are more remote and require 2 man hours and 3 man hours per ton respectively. Only 300 man hours are available, and all labour costs are fixed. At least 100 tons must be mined from the northern vein this week. The corporation must also yield at least 6000 kilograms of copper to meet contractual commitments.

Formulate SMC’s linear programming problem that can be used to determine the optimal number of tons that must be mined from each vein so as to maximize total revenue.

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