MATH 1071 LinearProgramming_11:5

If such a value exists it occurs at one or more

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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 Check-out: 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.

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