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Unformatted text preview: alue. If such a value exists, it
occurs at one or more corner points. Patrick Newberry Linear Programming November 5, 2012 9 / 14 Maximums and Minimums Notes Minimize Z = 3x + 2y on the feasible set shown here. has no maximum because z can get arbritraily
large minimum is 11 at point (1,4)
(x , y )
(0, 8)
(1, 4)
(4, 1)
(8, 0) Patrick Newberry Z = 3x + 2y
3(0) + 2(8) = 16
3(1) + 2(4) = 11
3(4) + 2(1) = 14
3(8) + 2(0) = 24 Linear Programming November 5, 2012 11 / 14 Maximums and Minimums Maximize: P = 100x + 200y
8
>20x + 30y 360
<
Subject to: 10x + 5y 100
>
:
x 0, y 0 Patrick Newberry Linear Programming Notes step 1: graph
step 2: test points
step 3: test the corners points
*dont forget to include 0 even though it's clear
it is not going to be the maximum November 5, 2012 12 / 14 finding points:
intercepts of contraints are (0,0), (10,0), (0,12)
for the other one you solve a system of equations
20x+30y=360
10x+5y+100
20y=160
y=8
x=6 Maximums and Minimums Notes (x , y )
P = 100x + 200y
(0, 0)
100(0) + 200(0) = 0
(0, 12) 100(0) + 200(12) = 2400
(6, 8)
100(6) + 200(8) = 2200
(10, 0) 100(10) + 200(0) = 1000 Patrick Newberry Linear Programming November 5, 2012 13 / 14 Maximums and Minimums Notes Clicker Checkout: Choose any letter to check out now.
Recitation Thursday: Quiz 5: Sections 6.4, 6.5, 6.6
Next Time: Continue Section 7.3 Applications of Linear Programming Patrick Newberry Linear Programming November 5, 2012 14 / 14...
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This document was uploaded on 02/18/2014 for the course MATH 1071 at Colorado.
 Fall '08
 MARSHALL,K
 Math, Linear Programming

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