Question
In: Advanced Math
Consider the following linear program. Maximize z= 5x1+ 3x2 subject to 3x1+ 5x2≤15 5x1+ 2x2≤10 –...
Consider the following linear program. Maximize z= 5x1+ 3x2
subject to 3x1+ 5x2≤15
5x1+ 2x2≤10
– x1+ x2≤2
x2≤2.5
x1≥0, x2≥0
a. Show the equality form of the model.
b. Sketch the graph of the feasible region and identify the extreme point solutions. From this representation find the optimal solution.
c. Analytically determine all solutions that derive from the intersection of two constraints or nonnegativity restrictions. Identify whether or not these solutions are feasible, and indicate the corresponding objective function values. Which one is optimal?
d.Let the slack variables for the first two constraints, x3and x4, be the axes of the graph, and sketch the geometric representation of the model. Show an iso-objective line in these variables, and from it determine the optimal solution.
Solutions
Colby Messinger answered 2 years agoRelated Solutions
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 linear programming problem: Max Z = 3x1 + 3x2 Subject to: ...
Consider the following linear programming problem:
Max Z =
3x1 + 3x2
Subject to: 10x1 +
4x2 ≤ 60
25x1 + 50x2 ≤ 200
x1, x2 ≥ 0
Find the optimal profit and the values of x1 and
x2 at the optimal solution.
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 ??
Consider the following linear program: maximize z = x1 + 4x2 subject to: x1 + 2x2...
Consider the following linear program:
maximize z = x1 + 4x2 subject to: x1 + 2x2 <= 13 x1 - x2 <= 8
- x1 + x2 <= 2
-3 <= x1 <= 8 -5 <= x2 <= 4
Starting with x1 and x2 nonbasic at their lower bounds, perform ONE
iteration of the Bounded Variables Revised Simplex Method. (Tableau
or matrix form is acceptable). Show your work. Clearly identify the
entering and leaving variables. After the pivot, identify the...
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.
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...
[6.4] Solve the following linear program by a graphical method: Maximize 3x1 + 3x2 + 21x3...
[6.4] Solve the following linear program by a graphical
method:
Maximize 3x1 + 3x2 + 21x3
subject to 6x1 + 9x2 + 25x3
<= 15
3x1 + 2x2 + 25x3 <= 20
x1 , x2 , x3 >= 0
(Hint: utilize the dual problem.)
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...
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