How many units of unused excess capacity in each plant

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Reference no: EM132172297

The ABC Company has three plants with excess production capacity. Fortunately, the company has a new product ready to begin production, and all three plants have the capability to produce this product with some of their excess capability. The product can be produced in three models - A, B, and C – that yield a net profit of $420, $360, and $300, respectively. Plants 1, 2, and 3 have the excess capacity to produce 750, 900, and 450 units per day of this product, respectively, regardless of the model or combination of the models involved.

The amount of a key material available at each plant location also limit the production of the product at each plant. Plants 1, 2, and 3 have 13,000, 12,000, and 5000 ounces, respectively, of the key material available for the production of this product each day. Each unit of model A, B, and C produced requires 20, 15, and 12 ounces of the material, respectively.

Sales forecasts indicate that if available, 900, 1200, and 750 units of the models A, B, C, respectively would be sold per day.

To balance the utilization of the excess production capacity of each plan, the management has decided that the plants should use the same percentage of their excess capacity to produce the new product. The company wishes to know how much of each model should be produced by each of the plants to maximize the profit.

a. Formulate the problem as a linear program in spreadsheet model.

b. Solve the problem using the Solver. How many units of each model is produced in each plant?

c. What is the profit from each plant in producing the new product each day? What is the total profit?

d. How many units of unused excess capacity in each plant?

e. If the balancing utilization constraint is not considered, what would the maximum total profit be?

f. For the optimal solution in e, how many units of unused excess capacity in each plant?

g. Compare the two solutions above (with and without the balancing constraint)

h. Express the original problem in algebraic form.

Reference no: EM132172297

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