Problem 2

A manufacturer has three plants with access production capacity. It can

use this capacity to produce a product that comes in three sizes, Large, Medium, and Small.

*The profit from selling the product depends on its size.

*The forecast of sales for each product size is known to be 900, 1200, 750 units for the Large, Medium and Small products respectively, so production levels should not exceed these values.

*There is a limited daily storage available in each plant, which limits the production levels in each plant.

*To prevent layoffs management wants the percent of the available capacity used for production be equal among all plants (for example, capacity in plant 1 is 750 units. If this plant produces 500 units, it uses 500/750 = .66 of its capacity. Then all plants should have the same percentage of their own capacities used)

Observe some more required information.

Plant1 Plant2 Plant3

Capacity avail 750 units 900 450

Storage avail 13000 sqft 12000 5000

Large Medium Small

Profit/unit $420 360 300

Storage/unit 20 sq-ft 15 12

2.1 Write the linear programming model