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 2 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...
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.
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...
Consider the following model: maximize 40x1 +50x2 subject to: x1 +2x2 ≤ 40 4x1 +3x2 ≤...
Consider the following model: maximize 40x1 +50x2 subject to: x1
+2x2 ≤ 40 4x1 +3x2 ≤ 120 x1, x2 ≥ 0 The optimal solution,
determined by the two binding constraints, is x1 = 24, x2 = 8, OFV∗
= 1,360. Now consider a more general objective function, c1x1 +
c2x2. Perform a sensitivity analysis to determine when the current
solution remains optimal in the following cases: (i) both
c1 and c2 may vary; (ii) c2 = 50, c1 may vary;...
"Primal" MAXIMIZE Z = 12X1 + 18X2 +10X3 S.T. 2X1 + 3X2 + 4X3 <= 50...
"Primal"
MAXIMIZE Z = 12X1 + 18X2 +10X3
S.T.
2X1 + 3X2 + 4X3 <= 50
-X1 + X2 + X3 <= 0
0X1 - X2 + 1.5X3 <= 0
X1, X2, X3 >=0
1. Write the "Dual" of this problem.
2. Write the "Dual of the Dual" of this problem.
For steps 3 & 4, use the Generic Linear Programming spreadsheet or the software of your choice.
(Submit a file pdf, text, xls file, etc., indicating the solution values...
[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 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 Z= 3 X1+4 X2+2.5X3 Subject to 3X1+4X2+2X3≤500 2X1+1X2+2X3≤400 1X1+3X2+3X3≤300 X1,X2,X3≥0 Change objective function coeffiecient x3...
Maximize Z= 3 X1+4 X2+2.5X3
Subject to
3X1+4X2+2X3≤500
2X1+1X2+2X3≤400
1X1+3X2+3X3≤300
X1,X2,X3≥0
Change objective function coeffiecient x3 to 6 and change
coefficient of x3 to 5in constraint 1 ,to 2 in constraint 2 ,to 4
in constraint3. calculate new optimal solution using sensitivity
analysis
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