1545 Words7 Pages

Simplex Method — more examples with standard problems
COPYRIGHT © 2006 by LAVON B. PAGE
Farmer problem (once again)
A farmer has a 320 acre farm on which she plants two crops: corn and soybeans. For each acre of corn planted, her expenses are $50 and for each acre of soybeans planted, her expenses are $100. Each acre of corn requires 100 bushels of storage and yields a profit of $60; each acre of soybeans requires 40 bushels of storage and yields a profit of $90. If the total amount of storage space available is 19,200 bushels and the farmer has only $20,000 on hand, how many acres of each crop should she plant in order to maximize her profit? What will her profit be if she follows this strategy?
COPYRIGHT © 2006 by LAVON B.*…show more content…*

How many houses of each type should he construct in order to maximize his profit? COPYRIGHT © 2006 by LAVON B. PAGE Planning Subdivision x = # townhouses y = # single story z = # 2-story COPYRIGHT © 2006 by LAVON B. PAGE Planning Subdivision x = # townhouses y = # single story z = # 2-story 1/6 x + 1/4 y + 1/2 z ! 60 40x + 50y + 60z ! 2880 25x + 30y + 40z ! 2400 Maximize: P = 15x + 18y + 20z (in thousands of $) COPYRIGHT © 2006 by LAVON B. PAGE 1/6 x + 1/4 y + 1/2 z ! 60 40x + 50y + 60z ! 2880 25x + 30y + 40z ! 2400 1/6 x + 1/4 y + 1/2 z + u = 60 40x + 50y + 60z + v = 2880 25x + 30y + 40z + w = 2400 –15x – 18y – 20z + P = 0 COPYRIGHT © 2006 by LAVON B. PAGE x ! 1 # # 6 # # 40 # # 25 # # -15 " y 1 4 50 30 -18 z 1 2 60 40 -20 u v w P 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 $ & 60 & & 2880 & & 2400 & & % 0 & Find the first pivot element. COPYRIGHT © 2006 by LAVON B. PAGE x ! 1 # # 6 # # 40 # # 25 # # -15 " y 1 4 50 30 -18 z 1 2 60 40 -20 u v w P 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 $ & 60 & & 2880 & & 2400 & & % 0 & Here is the first pivot element. What is the first row operation? COPYRIGHT © 2006 by LAVON B. PAGE x !1 # # 6 # #2 # # 3 # # 25 # # "-15 y 1 4 5 6 30 -18 z 1 2 u v w P 1 0 0 0 $ & 60 & & & 1 1 0 60 0 0 48 & & & 40 0 0 1 0 2400 & & & -20 0 0 0 1 0% Specify the row operations to finish this step. COPYRIGHT © 2006 by LAVON B. PAGE x ! -1

How many houses of each type should he construct in order to maximize his profit? COPYRIGHT © 2006 by LAVON B. PAGE Planning Subdivision x = # townhouses y = # single story z = # 2-story COPYRIGHT © 2006 by LAVON B. PAGE Planning Subdivision x = # townhouses y = # single story z = # 2-story 1/6 x + 1/4 y + 1/2 z ! 60 40x + 50y + 60z ! 2880 25x + 30y + 40z ! 2400 Maximize: P = 15x + 18y + 20z (in thousands of $) COPYRIGHT © 2006 by LAVON B. PAGE 1/6 x + 1/4 y + 1/2 z ! 60 40x + 50y + 60z ! 2880 25x + 30y + 40z ! 2400 1/6 x + 1/4 y + 1/2 z + u = 60 40x + 50y + 60z + v = 2880 25x + 30y + 40z + w = 2400 –15x – 18y – 20z + P = 0 COPYRIGHT © 2006 by LAVON B. PAGE x ! 1 # # 6 # # 40 # # 25 # # -15 " y 1 4 50 30 -18 z 1 2 60 40 -20 u v w P 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 $ & 60 & & 2880 & & 2400 & & % 0 & Find the first pivot element. COPYRIGHT © 2006 by LAVON B. PAGE x ! 1 # # 6 # # 40 # # 25 # # -15 " y 1 4 50 30 -18 z 1 2 60 40 -20 u v w P 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 $ & 60 & & 2880 & & 2400 & & % 0 & Here is the first pivot element. What is the first row operation? COPYRIGHT © 2006 by LAVON B. PAGE x !1 # # 6 # #2 # # 3 # # 25 # # "-15 y 1 4 5 6 30 -18 z 1 2 u v w P 1 0 0 0 $ & 60 & & & 1 1 0 60 0 0 48 & & & 40 0 0 1 0 2400 & & & -20 0 0 0 1 0% Specify the row operations to finish this step. COPYRIGHT © 2006 by LAVON B. PAGE x ! -1

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