Simplex Method Example - 1545 Words

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 ! -1Show MoreRelatedSimplex Method Essay1189 Words   |  5 PagesSimplex Method Paper Simplex Method Paper Many people may be wondering exactly what the simplex method is. The simplex method definition is a method for solving linear programming problems. According to Barnett, Byleen, and Karl (2011) the simplex method is used routinely on applied problems involving thousands of variables and problem constraints. George B. Dantzig developed the simplex method in 1947. In this paper the topic of discussion includes how to solve a simplex method problem thatRead MoreHw Solutions1306 Words   |  6 PagesTUTORIAL 2 Linear Programming - Minimisation Special cases Simplex maximisation 1. Innis Investments manages funds for a number of companies and wealthy clients. 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