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
rr rtsj idj rr rts−1. Since y is from the previous round, rts would be equal to rts−1
|0 |$ 60 |$ 0 |$ 60 |$ 0 |$ 0 |$ 0 |$ 0 |
System.out.println(); System.out.println("Total Sales \t Total Compensation"); System.out.println("----------- \t ------------------"); double minimumSales = 80000; double potentialCommission = minimumSales * 0.05; double potentialCommission1 = 85000 * 0.05; double potentialCommission2 = 90000 * 0.05; double potentialCommission3 = 95000 * 0.05; double potentialCommission4 = 100000 * 0.0625; double potentialCommission5 = 105000 * 0.0625; double potentialCommission6 = 110000 * 0.0625; double potentialCommission7 = 115000 * 0.0625; double potentialCommission8 = 120000 * 0.0625; double potentialCompensation = salary + potentialCommission; double potentialCompensation1 = salary + potentialCommission1; double potentialCompensation2 = salary + potentialCommission2; double potentialCompensation3 = salary + potentialCommission3; double potentialCompensation4 = salary + potentialCommission4; double potentialCompensation5 = salary + potentialCommission5; double potentialCompensation6 = salary + potentialCommission6; double potentialCompensation7 = salary + potentialCommission7; double potentialCompensation8 = salary + potentialCommission8;
5 x 2 + -6 x 4 + 5 x 8 + -6 x 1= 10 -24 + 40 -6= 20
0 1 1 0 0 0 0 1 64+32+1=97, This is the ASCII code for A
P B - 2 0 0 6 - 2 | M a y 17, 2 0 0 6
5.000,00 $ 7.500 151.250 20 35.000,00 $ 12.500 321.250 26 $ 58,20 $ 110.000,00 4.000 333.500 83 115,38
1,300 1,200 1,100 1,000 900 800 700 600 500 400 300 200 100 0 0 5,000 10,000 15,000 20,000 25,000
The Wiethoff Company has a contract to produce 10000 garden hoses for a customer. Wiethoff has 4 different machines that can produce this kind of hose. Because these machines are from different manufacturers and use differing technologies, their specifications are not the same.
665 0.34 174 216 537 234 122 1.2 0.2 60.4 9.6 0.22 65.0 2,149 554 66.6 2,483 80,300 492 14 23 6 21 15 874 524 12,216 30
∏i = (Pe + 40 - 100) x 100 = 100 x Pe –6,000 -------------------- [1]
(0.94,0) 0.85(0.94) + 0.65(0) = $0.799 3) Linear Programing Model Decision Variables: Let a = Automobile Loans Let f = Furniture Loans Let o = Other Secured Loans Let s = Signature Loans Let r = Risk-free Securities Objective Function: Maximize Z = 0.8a + 0.1f + 0.11o + 0.12s + 0.9r where Z =
2(X4 + X5 + X6 + X7 + X10 + X11 + X16 + X17 + X18 + X27 + X28) – (X1 + X2 +X3