Consider the following linear program. Min 8X + 12Y s.t. 1X + 3Y 28 2X + 2Y 2 12 6x + 2Y 2 16 X, Y 20 (a) Use the graphical solution procedure to find the optimal solution. What is the value of the objective function at the optimal solution? 52 ✔at (x, y) =(2,3 (b) Assume that the objective function coefficient for X changes from 8 to 6. Use the graphical solution procedure to find the new optimal solution. Does the optimal solution change? The extreme point (x, y) = 2,3 x X X remains ✔✔✔ optimal. The value of the objective function becomes 48 (c) Assume that the objective function coefficient for X remains 8, but the objective function coefficient for Y changes from 12 to 6. Use the graphical solution procedure to find the new optimal solution. Does the optimal solution change? The extreme point (x, y) = 3,2 x. becomes ✔✔✔ optimal. The value of the objective function becomes 36 x.
Consider the following linear program. Min 8X + 12Y s.t. 1X + 3Y 28 2X + 2Y 2 12 6x + 2Y 2 16 X, Y 20 (a) Use the graphical solution procedure to find the optimal solution. What is the value of the objective function at the optimal solution? 52 ✔at (x, y) =(2,3 (b) Assume that the objective function coefficient for X changes from 8 to 6. Use the graphical solution procedure to find the new optimal solution. Does the optimal solution change? The extreme point (x, y) = 2,3 x X X remains ✔✔✔ optimal. The value of the objective function becomes 48 (c) Assume that the objective function coefficient for X remains 8, but the objective function coefficient for Y changes from 12 to 6. Use the graphical solution procedure to find the new optimal solution. Does the optimal solution change? The extreme point (x, y) = 3,2 x. becomes ✔✔✔ optimal. The value of the objective function becomes 36 x.
Chapter4: Systems Of Linear Equations
Section4.3: Solve Mixture Applications With Systems Of Equations
Problem 158E: The manufacturer of an energy drink spends $1.20 to make each drink and sells them for $2. The...
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Transcribed Image Text:Consider the following linear program.
Min 8X + 12Y
s.t.
1X + 3Y 28
2X + 2Y 212
6X + 2Y 2 16
X, Y 20
(a) Use the graphical solution procedure to find the optimal solution.
What is the value of the objective function at the optimal solution?
2,3
52
(b) Assume that the objective function coefficient for X changes from 8 to 6. Use the graphical solution procedure to find the new optimal solution.
Does the optimal solution change?
The extreme point (X, Y) = 2,3
at (x, y) =
Variable
X
Y
(c) Assume that the objective function coefficient for X remains 8, but the objective function coefficient for Y changes from 12 to 6. Use the graphical solution procedure to find the new optimal solution.
Does the optimal solution change?
The extreme point (X,Y)= 3,2
8.00000
12.00000
X
4.00000
X
(d) The computer solution for the linear program in part (a) provides the following objective coefficient range information.
Objective Allowable
Coefficient Increase
Allowable
Decrease
12.00000
X
remains ✓✓
becomes
optimal. The value of the objective function becomes 48
4.00000
4.00000
✔ optimal. The value of the objective function becomes 36
How would this objective coefficient range information help you answer parts (b) and (c) prior to re-solving the problem?
The objective coefficient range for variable X is 4
to 8
4
X to 12
X. Since the change in part (c) is outside
X . Since the change in part (b) is within
|× .
✔
this range, we know the optimal solution will
x .
this range, we know the optimal solution will not
change.
✓ change. The objective coefficient range for variable Y is
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Follow-up Question
Transcribed Image Text:(d) The computer solution for the linear program in part (a) provides the following objective coefficient range information.
Objective Allowable Allowable
Coefficient Increase Decrease
Variable
Y
8.00000
12.00000
4.00000
12.00000
4.00000
4.00000
How would this objective coefficient range information help you answer parts (b) and (c) prior to re-solving the problem?
The objective coefficient range for variable X is 4
X. Since the change in part (b) is within
4
X to 12
✔ this range, we know the optimal solution
to 8
X. Since the change in part (c) is outside
will
this range, we know the optimal solution will not
change.
change. The objective coefficient range for variable Y is
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