Minimize Z = 200x| + 160x2 (cost, $) subject to 6x1 + 2x2 2 12 (high-grade ore, tons) 2x1 + 2x2 2 8 (medium-grade ore, tons) 4x1 + 12x2 2 24 (low-grade ore, tons) X1, X2 2 ()

Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter7: Nonlinear Optimization Models
Section: Chapter Questions
Problem 67P
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The Copperfield Mining Company owns two mines,which produce three grades of ore: high, medium, andlow. The company has a contract to supply a smeltingcompany with 12 tons of high-grade ore, 8 tons ofmedium-grade ore, and 24 tons of low-grade ore. Eachmine produces a certain amount of each type of ore eachhour it is in operation. The company has developed thefollowing linear programming model to determine thenumber of hours to operate each mine (x1 and x2) so thatcontracted obligations can be met at the lowest cost:a. Solve this model graphically.b. Solve the model using Excel.

Minimize Z = 200x| + 160x2 (cost, $)
subject to
6x1 + 2x2 2 12 (high-grade ore, tons)
2x1 + 2x2 2 8 (medium-grade ore, tons)
4x1 + 12x2 2 24 (low-grade ore, tons)
X1, X2 2 ()
Transcribed Image Text:Minimize Z = 200x| + 160x2 (cost, $) subject to 6x1 + 2x2 2 12 (high-grade ore, tons) 2x1 + 2x2 2 8 (medium-grade ore, tons) 4x1 + 12x2 2 24 (low-grade ore, tons) X1, X2 2 ()
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