3.21. The Weigelt Corporation has three branch plants with excess production capacity. Fortunately, the corporation has a new product ready to begin production, and all three plants have this capability, so some of the excess capacity can be used in this way. This product can be made in three sizes- large, medium, and small-that yield a net unit 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 size or combination of sizes involved. The amount of available in-process storage space also imposes a limitation on the production rates of the new product. Plants 1, 2, and 3 have 13,000, 12,000, and 5,000 square feet, respectively, of in-process storage space available for a day's production of this product. Each unit of the large, medium, and small sizes produced per day requires 20, 15, and 12 square feet, respectively. Sales forecasts indicate that if available, 900, 1,200, and 750 units of the large, medium, and small sizes, respectively, would be sold per day. At each plant, some employees will need to be laid off unless most of the plant's excess production capacity can be used to produce the new product. To avoid layoffs if possible, manage- ment has decided that the plants should use the same percentage of their excess capacity to produce the new product. Management wishes to know how much of each of the sizes should be produced by each of the plants to maximize profit. a. Formulate and solve a linear programming model for this mixed problem on a spreadsheet. b. Express the model in algebraic form.
3.21. The Weigelt Corporation has three branch plants with excess production capacity. Fortunately, the corporation has a new product ready to begin production, and all three plants have this capability, so some of the excess capacity can be used in this way. This product can be made in three sizes- large, medium, and small-that yield a net unit 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 size or combination of sizes involved. The amount of available in-process storage space also imposes a limitation on the production rates of the new product. Plants 1, 2, and 3 have 13,000, 12,000, and 5,000 square feet, respectively, of in-process storage space available for a day's production of this product. Each unit of the large, medium, and small sizes produced per day requires 20, 15, and 12 square feet, respectively. Sales forecasts indicate that if available, 900, 1,200, and 750 units of the large, medium, and small sizes, respectively, would be sold per day. At each plant, some employees will need to be laid off unless most of the plant's excess production capacity can be used to produce the new product. To avoid layoffs if possible, manage- ment has decided that the plants should use the same percentage of their excess capacity to produce the new product. Management wishes to know how much of each of the sizes should be produced by each of the plants to maximize profit. a. Formulate and solve a linear programming model for this mixed problem on a spreadsheet. b. Express the model in algebraic form.
Practical Management Science
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ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
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Transcribed Image Text:3.21. The Weigelt Corporation has three branch plants with
excess production capacity. Fortunately, the corporation has
a new product ready to begin production, and all three plants
have this capability, so some of the excess capacity can be
used in this way. This product can be made in three sizes-
large, medium, and small-that yield a net unit 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 size or combination of
sizes involved.
The amount of available in-process storage space also
imposes a limitation on the production rates of the new product.
Plants 1, 2, and 3 have 13,000, 12,000, and 5,000 square feet,
respectively, of in-process storage space available for a day's
production of this product. Each unit of the large, medium, and
small sizes produced per day requires 20, 15, and 12 square feet,
respectively.
Sales forecasts indicate that if available, 900, 1,200, and 750
units of the large, medium, and small sizes, respectively, would
be sold per day.
At each plant, some employees will need to be laid off unless
most of the plant's excess production capacity can be used to
produce the new product. To avoid layoffs if possible, manage-
ment has decided that the plants should use the same percentage
of their excess capacity to produce the new product.
Management wishes to know how much of each of the sizes
should be produced by each of the plants to maximize profit.
a. Formulate and solve a linear programming model
for this mixed problem on a spreadsheet.
b. Express the model in algebraic form.
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