Convert the follow system of equations to standard form and
solve using Simplex method to find optimal solution
Maximize 10.75x + 5.3y
constraints
0.25x + 0.6y < = 1000
0.50x + 0.1y <= 1000
0.25x + 0.3y <= 1000
x>=250, y>=250
consider the following LP
a. put the problem into standard form, using slack, excess, and
artificial variables
b. solve the associated LP of phase I
c. is w'=0, proceed to phase 2 and solve the original LP. show
all of the work.
max z=x1-x2+3x3
S.T. x1+x2<=20
x2+x3>=10
x1+x3=5
x1,x2>=0
Using the information below to create the initial simplex
matrix. Assume all variables are nonnegative.
Maximize f=9x1+4x2+10x3f=9x1+4x2+10x3 subject to
9x1+6x2+2x3?459x1+6x2+2x3?45
7x1+8x2+10x3?707x1+8x2+10x3?70
8x1+9x2+11x3?658x1+9x2+11x3?65
x1?0x1?0
x2?0x2?0
x3?0x3?0
2. Convert the following infix form expression into the postfix
form expression by using a stack:
A+(B*(C-D)+E)/F-G*H
Show the stack after each push/pop.
Solve the following problem using the simplex method. If the
problem is two dimensional, graph the feasible region, and outline
the progress of the algorithm.
Max
Z = 5X1 + 3X2 +
2X3
Subject to 4X1 + 5X2 +
2X3 + X4≤ 20
3X1 + 4X2 - X3 + X4≤ 30
X1, X2, X3, X4 ≥
0
Solve the following problem using both graphical method and
Simplex tableau
Maximize f(x,y)=5x+4y subject to 3x+5y<=180 where 28 => x
=> 0 and 30=> y=>0
Find the optimum solution to the following LP using the Simplex
Algorithm. Use Two-Phase method.
??? ?=3?2+2?3 ??
−2?1 + ?2 − ?3 ≤ −3
−?1 + 2?2 + ?3 = 6
?1,?2,?3 ≥0