Question
In: Statistics and Probability
Maximize $4X1 + $8X2 Subject To 2X1 + 5X2 ≤ 50 3X1 + 3X2 ≤ 48...
Maximize $4X1 + $8X2
Subject To 2X1 + 5X2 ≤ 50
3X1 + 3X2 ≤ 48
X1, X2 ≥ 0
what the optimal ??
Solutions
orchestra answered 3 years agoRelated Solutions
Consider the following linear programming problem Maximize $4X1 + $5X2 Subject To 2X1 + 5X2 ≤...
Consider the following linear programming problem
Maximize
$4X1 + $5X2
Subject To
2X1 + 5X2 ≤ 40 hr
Constraint A
3X1 + 3X2 ≤ 30 hr
Constraint B
X1, X2 ≥ 0
Constraint C
if A and B are the two binding constraints.
(Round to ONLY two digits after decimal
points)
a) What is the range of optimality of
the objective function?
Answer ≤ C1/C2 ≤ Answer
b) Suppose that the unit revenues for X1 and X2 are changed to
$100 and...
Consider the following linear programming problem Maximize $4X1 + $5X2 Subject To 2X1 + 5X2 ≤...
Consider the following linear programming problem
Maximize
$4X1 + $5X2
Subject To
2X1 + 5X2 ≤ 40 hr
Constraint A
3X1 + 3X2 ≤ 30 hr
Constraint B
X1, X2 ≥ 0
Constraint C
if A and B are the two binding constraints.
(Round to ONLY two digits after decimal
points)
a) What is the range of optimality of
the objective function?
.......... ≤
C1/C2 ≤ ............
b) Suppose that the unit revenues for X1 and X2 are changed to
$100 and...
Consider the following problem Maximize Z=2x1 + 5x2 + x3 subject to 4x1+...
Consider the following problem
Maximize Z=2x1 + 5x2 +
x3
subject to
4x1+ 2x2 + x3 ≤ 6
x1 + x2 ≤ 2
xi ≥ 0 for i=1,2,3
a. Inserting slack variables, construct the initial simplex
tableau. What is the initial basic feasible solution?
b. What is the next non-basic variable to enter the basis
c. Using the minimum ratio rule, identify the basic variable to
leave the basis.
d. Using elementary row operations, find...
maximize z = 2x1+3x2 subject to x1+3X2 6 3x1+2x2 6 &nb
maximize z = 2x1+3x2
subject to x1+3X2 6
3x1+2x2 6
x1,x2
This can be simply done by drawing all the lines in the x-y
plane and looking at the corner points.
Our points of interest are the corner points and we will check
where we get the maximum value for our objective function by
putting all the four corner points. (2,0), (0,2), (0,0), (6/7,
12/7)
We get maximum at = (6/7, 12/7) and the maximum value is =...
Consider the following problem Maximize Z=2x1 + 5x2 + x3 subject to 4x1+ 2x2...
Consider the following problem
Maximize Z=2x1 + 5x2 +
x3
subject to
4x1+ 2x2 + x3 ≤ 6
x1 + x2 ≤ 2
xi ³ 0 for i=1,2,3
a. Inserting slack variables, construct the initial simplex
tableau. What is the initial basic feasible solution?
b. What is the next non-basic variable to enter the basis
c. Using the minimum ratio rule, identify the basic variable to
leave the basis.
d. Using elementary row operations, find the...
Consider the following problem Maximize Z=2x1 + 5x2 subject to 4x1+ 2x2 ≤ 6...
Consider the following problem
Maximize Z=2x1 +
5x2
subject to
4x1+ 2x2 ≤ 6
x1 + x2 ≥ 2
xi ≥0 for i=1,2
Inserting slack, excess, or artificial variables, construct the
initial simplex tableau.
Identify the corresponding initial (artificial) basic feasible
solution including the objective function value.
Identify the entering basic variable and the leaving basic
variable for the next iteration.
MAX Z = 2x1 + 8x2 + 4x3 + 9x4 subject to 2x1 + 3x2 +...
MAX Z = 2x1 + 8x2 + 4x3 + 9x4
subject to
2x1 + 3x2 + 2x4 <= 8
2x2 + 5x3 + x4 <= 12
3x1 + x2 + 4x3 + 2x4 <= 15
and x1,x2,x3,x4 >= 0
apply the Primal Simplex Method to recover
optimality.
Max Z = 2x1 + 8x2 + 4x3 subject to 2x1 + 3x2 ≤ 8 2x2...
Max Z = 2x1 + 8x2 + 4x3
subject to
2x1 + 3x2 ≤ 8
2x2 + 5x3 ≤ 12
3x1 + x2 +
4x3
≤15
and x1,x2,x3≥0;
Indicate clearly the optimal basic and nonbasic
variables and their values and write the reduced cost of each
optimal nonbasic variable.
MAX Z = 2x1 + 8x2 + 4x3 subject to 2x1 + 3x2 <= 8 2x2...
MAX Z = 2x1 + 8x2 + 4x3
subject to
2x1 + 3x2 <= 8
2x2 + 5x3 <= 12
3x1 + x2 + 4x3 <= 15
x1 + x3 = 11
and x1,x2,x3 >= 0
apply the Dual Simplex Method to recover
feasibility.
Max Z = 2x1 + 8x2 + 4x3 subject to 2x1 + 3x2 ≤ 8 2x2...
Max Z = 2x1 + 8x2 + 4x3
subject to
2x1 + 3x2 ≤ 8
2x2 + 5x3 ≤ 12
3x1 + x2 +
4x3
≤15
and x1,x2,x3≥0;
Solve the LP you create by using the Simplex Method. You
can use Big-M or Two-Phase Method if needed
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