A certain corporation has three plants with excess production capacity.

A certain corporation has three plants with excess production capacity. All the three plants have the capability of producing certain products, and the management has decided to use the excess capacity in this way. This product can be made in three sizes-large medium and small, which yield a net profit of $1200, 100 and 900 respectively. Plant 1,2 & 3 has excess manpower and equipment capacity to produce 55,600 and 300 units per day of these products respectively regardless of the sizes of combination of sizes involved.However,the amount available in process storage space also impose a limitation of production rate .plants 1,2 and 3 have 900,8000 and 5000 square feet in process storage space available for the product .each unit of large, medium and small sizes produced per day require 20,15 and 12 squire feet respectivelty.Sales forecast indicates that 600,800 and 500 units of large, medium and small sizes can be sold per day. In order to maintain a uniform workload among the plants and retain some flexibility, the management has decided that additional production assigned to each plant must use the same percentage of excess manpower and equipment capacity. Management wishes to know how much of each size should be produced by each of the plant in order to maximize profit. solve the problem using simplex method

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