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The Weigelt Corporation has three branch plants with excessproduction capacity. Fortunately, the corporation has a new productready to begin production, and all three plants have thiscapability, so some of the excess capacity can be used in this way.This product can be made in three sizes--large, medium, andsmall--that yield a net unit profit of $420, $360, and $300,respectively. Plants 1, 2, and 3 have the excess capacity toproduce 750, 900, and 450 units per day of this product,respectively, regardless of the size or combination of sizesinvolved.

The amount of available in-process storage space also imposes alimitation on the production rates of the new product. Plants 1, 2,and 3 have 13,000, 12,000, and 5,000 square feet, respectively, ofin-process storage space available for a day's production of thisproduct. Each unit of the large, medium, and small sizes producedper day requires 20, 15, and 12 square feet, respectively.

Sales forecasts indicate that if available, 900, 1,200, and 750units of the large, medium, and small sizes, respectively, would besold per day.

At each plant, some employees will need to be laid off unlessmost of the plant’s excess production capacity can be used toproduce the new product. To avoid layoffs if possible, managementhas decided that the plants should use the same percentage of theirexcess capacity to produce the new product.

Management wishes to know how much of each of the sizes shouldbe produced by each of the plants to maximize profit.

1. Formulate the dual of the above problem and solve it.

2. Weigelt.lp

   /* objective function */

   Max: 420 L1 + 360 M1 + 300 S1 + 420 L2 + 360 M2 + 300 S2 + 420L3 + 360 M3 + 300 S3;

   /* Constraints */

   /* capacity */

   L1 + M1 + S1 <= 750;

   L2 + M2 + S2 <= 900;

   L3 + M3 + S3 <= 450;

   /* square footage */

   20 L1 + 15 M1 + 12 S1 <= 13000;

   20 L2 + 15 M2 + 12 S2 <= 12000;

   20 L3 + 15 M3 + 12 S3 <= 5000;

   /* sales */

   L1 + L2 + L3 <= 900;

   M1 + M2 + M3 <= 1200;

   S1 + S2 + S3 <= 750;

   /* same percentage of capacity */

   900 L1 + 900 M1 + 900 S1 - 750 L2 - 750 M2 - 750 S2 = 0;

   450 L1 + 450 M1 + 450 S1 - 750 L3 - 750 M3 - 750 S3 = 0;

   * Formulate the dual of the above problem and solve it. I justneed help with the dual formulation of this LP solution.