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A manufacturer produces bicycles and motorcycles, each of which must be processed through two machine centers. Machine center 1 has a maximum of 120 hours available and machine center 2 has a maximum of 180 hours available.  A bicycle requires 6 hours in mc1 and 3 hours in mc2.  Manufacturing a motorcycle requires 4 hours in mc1 and 10 hours in mc2.  If the profit is $45 for each bicycle and $250 for a motorcycle, determine the number of bicycles and number of motorcycles to produce to maximize profit considering that the number of motorcycles must not exceed 12 units and bicycle must be at least 10 units.  Formulate as Linear Program and solve using the graphical Method.

A manufacturer produces bicycles and motorcycles, each of which must be processed through two machine centers. Machine center 1 has a maximum of 120 hours available and machine center 2 has a maximum of 180 hours available.  A bicycle requires 6 hours in mc1 and 3 hours in mc2.  Manufacturing a motorcycle requires 4 hours in mc1 and 10 hours in mc2.  If the profit is $45 for each bicycle and $250 for a motorcycle, determine the number of bicycles and number of motorcycles to produce to maximize profit considering that the number of motorcycles must not exceed 12 units and bicycle must be at least 10 units.  Formulate as Linear Program and solve using the graphical Method.

Practical Management Science
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter3: Introduction To Optimization Modeling
Section: Chapter Questions
Problem 38P
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  1. A manufacturer produces bicycles and motorcycles, each of which must be processed through two machine centers. Machine center 1 has a maximum of 120 hours available and machine center 2 has a maximum of 180 hours available.  A bicycle requires 6 hours in mc1 and 3 hours in mc2.  Manufacturing a motorcycle requires 4 hours in mc1 and 10 hours in mc2.  If the profit is $45 for each bicycle and $250 for a motorcycle, determine the number of bicycles and number of motorcycles to produce to maximize profit considering that the number of motorcycles must not exceed 12 units and bicycle must be at least 10 units.  Formulate as Linear Program and solve using the graphical Method.

  2. Solve using LP-Simplex Solution

                Maximize Z = 10X1 + 14X2

                Subject to:

                            4x1 + 6x2 <= 24

                            2x1 + 6x2 <= 20

                               x1, x2 >= 0

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