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Practical Management Science

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter12: Queueing Models

Section: Chapter Questions

Problem 59P

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Hi, I'm trying to understand why the number of hours for the shaper and the grinder were multiplied by 60 (circled in red). Can I please have some help? Thanks!

Objective Functions and Constraints:
Based on the given details, the objective functions and constraints are
Objective Function:
Max Z = 8 A + 6B + 9C
Decision Variables:
A - Component 1
B - Component 2
C - Component 3
Constraints:
Subject to
Shaper 6A + 4B + 4C ≤(120*60)
Grinder 4 A + 5B + 2C (110 * 60)
Component 3: C ≤ 200
Component 1: A ≤ 900
Component 2: B ≤ 900
Component 1 has orders: A ≥ 600
Non negativity: A, B, C ≥ 0

Vollmer Manufacturing makes three components for sale to refrigeration companies. The components are processed on two machines: a shaper and a grinder.
The times (in minutes) required on each machine are as follows:
Component
1
2
3
Shaper
6
4
Machine
4
Grinder
4
5
2
The shaper is available for 120 hours, and the grinder is available for 110 hours. No more than 200 units of component 3 can be sold, but up to 900 units of each
of the other components can be sold. In fact, the company already has orders for 600 units of component 1 that must be satisfied. The profit contributions for
components 1, 2, and 3 are $8, $6, and $9, respectively.

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