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Test Bank Introduction to Operations Research 11th Edition by Frederick S. Hillier, Gerald J. Lieberman Chapter 3-28|Complete Guide A$10.98
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Test Bank for Chapter 3
Problem 3-1:
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,
management 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.
Formulate a linear programming model for this problem.
, However, any one of the three equality constraints is redundant, so any one (say, this one) can be
deleted.
Problem 3-2:
Comfortable Hands is a company which features a product line of winter gloves for the entire
family — men, women, and children. They are trying to decide what mix of these three types of
gloves to produce.
Comfortable Hands’ manufacturing labor force is unionized. Each full-time employee
works a 40-hour week. In addition, by union contract, the number of full-time employees can
never drop below 20. Nonunion, part-time workers can also be hired with the following union-
imposed restrictions: (1) each part-time worker works 20 hours per week, and (2) there must be
at least 2 full-time employees for each part-time employee.
All three types of gloves are made out of the same 100% genuine cowhide leather.
Comfortable Hands has a long term contract with a supplier of the leather, and receives a 5,000
square feet shipment of the material each week. The material requirements and labor
requirements, along with the gross profit per glove sold (not considering labor costs) is given in
the following table.
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