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Operations Management
Carco uses robots to manufacture cars. The followingdemands for cars must be met (not necessarily on time, butall demands must be met by end of quarter 4): quarter 1—600; quarter 2—800; quarter 3—500; quarter 4—400. Atthe beginning of the quarter, Carco has two robots. Robotscan be purchased at the beginning of each quarter, but amaximum of two per quarter can be purchased. Each robotcan build as many as 200 cars per quarter. It costs $5,000to purchase a robot. Each quarter, a robot incurs $500 inmaintenance costs (even if it is not used to build any cars).Robots can also be sold at the beginning of each quarter for$3,000. At the end of each quarter, a holding cost of $200per car is incurred. If any demand is backlogged, then a costof $300 per car is incurred for each quarter the demand isbacklogged.At the end of quarter 4, Carco must have at least two robots. Formulate an LP to minimize the total cost incurred inmeeting the next four quarters’ demands for cars.

Carco uses robots to manufacture cars. The followingdemands for cars must be met (not necessarily on time, butall demands must be met by end of quarter 4): quarter 1—600; quarter 2—800; quarter 3—500; quarter 4—400. Atthe beginning of the quarter, Carco has two robots. Robotscan be purchased at the beginning of each quarter, but amaximum of two per quarter can be purchased. Each robotcan build as many as 200 cars per quarter. It costs $5,000to purchase a robot. Each quarter, a robot incurs $500 inmaintenance costs (even if it is not used to build any cars).Robots can also be sold at the beginning of each quarter for$3,000. At the end of each quarter, a holding cost of $200per car is incurred. If any demand is backlogged, then a costof $300 per car is incurred for each quarter the demand isbacklogged.At the end of quarter 4, Carco must have at least two robots. Formulate an LP to minimize the total cost incurred inmeeting the next four quarters’ demands for cars.

Practical Management Science
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter4: Linear Programming Models
Section: Chapter Questions
Problem 87P
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Carco uses robots to manufacture cars. The following
demands for cars must be met (not necessarily on time, but
all demands must be met by end of quarter 4): quarter 1—
600; quarter 2—800; quarter 3—500; quarter 4—400. At
the beginning of the quarter, Carco has two robots. Robots
can be purchased at the beginning of each quarter, but a
maximum of two per quarter can be purchased. Each robot
can build as many as 200 cars per quarter. It costs $5,000
to purchase a robot. Each quarter, a robot incurs $500 in
maintenance costs (even if it is not used to build any cars).
Robots can also be sold at the beginning of each quarter for
$3,000. At the end of each quarter, a holding cost of $200
per car is incurred. If any demand is backlogged, then a cost
of $300 per car is incurred for each quarter the demand is
backlogged.
At the end of quarter 4, Carco must have at least two robots. Formulate an LP to minimize the total cost incurred in
meeting the next four quarters’ demands for cars.

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ISBN:
9781337406659
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