A company must meet (on time) the following demands:quarter 1—30 units; quarter 2—20 units; quarter 3—40units. Each quarter, up to 27 units can be produced withregular-time labor, at a cost of $40 per unit. During eachquarter, an unlimited number of units can be produced withovertime labor, at a cost of $60 per unit. Of all unitsproduced, 20% are unsuitable and cannot be used to meetdemand. Also, at the end of each quarter, 10% of all unitson hand spoil and cannot be used to meet any futuredemands. After each quarter’s demand is satisfied andspoilage is accounted for, a cost of $15 per unit is assessedagainst the quarter’s ending inventory. Formulate an LP thatcan be used to minimize the total cost of meeting the nextthree quarters’ demands. Assume that 20 usable units areavailable at the beginning of quarter 1.

A company must meet (on time) the following demands:quarter 1—30 units; quarter 2—20 units; quarter 3—40units. Each quarter, up to 27 units can be produced withregular-time labor, at a cost of $40 per unit. During eachquarter, an unlimited number of units can be produced withovertime labor, at a cost of $60 per unit. Of all unitsproduced, 20% are unsuitable and cannot be used to meetdemand. Also, at the end of each quarter, 10% of all unitson hand spoil and cannot be used to meet any futuredemands. After each quarter’s demand is satisfied andspoilage is accounted for, a cost of $15 per unit is assessedagainst the quarter’s ending inventory. Formulate an LP thatcan be used to minimize the total cost of meeting the nextthree quarters’ demands. Assume that 20 usable units areavailable at the beginning of quarter 1.

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter2: Introduction To Spreadsheet Modeling

Section: Chapter Questions

Problem 33P: Assume the demand for a companys drug Wozac during the current year is 50,000, and assume demand...

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Concept explainers

Optimization Models

Optimization models are mathematical models that help organizations determine the best way to allocate scarce resources to achieve specific objectives. These models can be used to solve a wide variety of problems, from finding the most efficient route for a delivery truck to determining the optimal mix of products to stock in a store.

Question

A company must meet (on time) the following demands:
quarter 1—30 units; quarter 2—20 units; quarter 3—40
units. Each quarter, up to 27 units can be produced with
regular-time labor, at a cost of $40 per unit. During each
quarter, an unlimited number of units can be produced with
overtime labor, at a cost of $60 per unit. Of all units
produced, 20% are unsuitable and cannot be used to meet
demand. Also, at the end of each quarter, 10% of all units
on hand spoil and cannot be used to meet any future
demands. After each quarter’s demand is satisfied and
spoilage is accounted for, a cost of $15 per unit is assessed
against the quarter’s ending inventory. Formulate an LP that
can be used to minimize the total cost of meeting the next
three quarters’ demands. Assume that 20 usable units are
available at the beginning of quarter 1.

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