A garden store prepares various grades of pine bark for mulch: nuggets (x1), mini-nuggets (x2),and chips (x3). The process requires pine bark, machine time, labor time, and storage space. Thefollowing model has been developed.Maximize Z = 9 x1 + 9x2 + 6x3 (profit)Subject toBark 5x1 + 6x2 + 3x3 ≤ 600 pounds Machine 2x1 + 4x2 + 5x3 ≤ 600 minutesLabor 2x1 + 4x2 + 3x3 ≤ 480 hoursStorage 1x1 + 1x2 + 1x3 ≤ 150 bags x1, x2, x3 ≥ 0 a. What is the marginal value of a pound of pine bark? Over what range is this price valueappropriate?
A garden store prepares various grades of pine bark for mulch: nuggets (x1), mini-nuggets (x2),and chips (x3). The process requires pine bark, machine time, labor time, and storage space. Thefollowing model has been developed.Maximize Z = 9 x1 + 9x2 + 6x3 (profit)Subject toBark 5x1 + 6x2 + 3x3 ≤ 600 pounds Machine 2x1 + 4x2 + 5x3 ≤ 600 minutesLabor 2x1 + 4x2 + 3x3 ≤ 480 hoursStorage 1x1 + 1x2 + 1x3 ≤ 150 bags x1, x2, x3 ≥ 0 a. What is the marginal value of a pound of pine bark? Over what range is this price valueappropriate?
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter5: Network Models
Section: Chapter Questions
Problem 67P
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A garden store prepares various grades of pine bark for mulch: nuggets (x1), mini-nuggets (x2),
and chips (x3). The process requires pine bark, machine time, labor time, and storage space. The
following model has been developed.
Maximize Z = 9 x1 + 9x2 + 6x3 (profit)
Subject to
Bark 5x1 + 6x2 + 3x3 ≤ 600 pounds
Machine 2x1 + 4x2 + 5x3 ≤ 600 minutes
Labor 2x1 + 4x2 + 3x3 ≤ 480 hours
Storage 1x1 + 1x2 + 1x3 ≤ 150 bags
x1, x2, x3 ≥ 0
a. What is the marginal value of a pound of pine bark? Over what range is this price value
appropriate?
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