Question
In: Advanced Math
3. Solve the following linear programming problem. You must use the dual. First write down the...
3. Solve the following linear programming problem. You must use the dual. First write down the dual maximization LP problem, solve that, then state the solution to the original minimization problem.
(a) Minimize w = 4y1 + 5y2 + 7y3
Subject to: y1 + y2 + y3 ≥ 18
2y1 + y2 + 2y3 ≥ 20
y1 + 2y2 + 3y3 ≥ 25
y1, y2, y3 ≥ 0
(b) Making use of shadow costs, if the 2nd original constraint changed to
2y1 + y2 + 2y3 ≥ 24, now what will the minimum of w be? Explain clearly.
(c) Making use of shadow costs, if the 1st original constraint changed to
y1 + y2 + y3 21, now what will the minimum of w be? Explain clearly.
Solutions
Colby Messinger answered 1 year agoRelated Solutions
Solve the following linear programming problem. You must use the dual. First write down the dual...
Solve the following linear programming problem. You must
use the dual. First write down the dual maximization LP problem,
solve that, then state the solution to the original minimization
problem.
(a) Minimize w = 4y1 +
5y2 + 7y3
Subject to: y1 + y2 + y3 ≥
18
2y1 + y2 + 2y3 ≥ 20
y1 + 2y2 + 3y3 ≥ 25
y1, y2, y3 ≥ 0
(b) Making use of shadow costs, if the
2nd original constraint changed to...
Solve the following linear programming problem using the dual simplex method: max ? = −?1 −...
Solve the following linear programming problem using the dual
simplex method:
max ? = −?1 − 2?2
s.t.
−2?1 + 7?2 ≤ 6
−3?1 + ?2 ≤ −1
9?1 − 4?2 ≤ 6
?1 − ?2 ≤ 1
7?1 − 3?2 ≤ 6
−5?1 + 2?2 ≤ −3
?1,?2 ≥ 0
Use the dual simplex method to solve the following linear programming problems. Clearly indicate all the...
Use the dual simplex method to solve the following linear
programming problems. Clearly indicate all the steps, the entering
and departing rows and columns and rows, the pivot and the row
operations used. Use the simplex method to solve the following
linear programming problems. Clearly indicate all the steps, the
entering and departing rows and columns and rows, the pivot and the
row operations used. 2.2.1 An electronics manufacturing company has
three production plants, each of which produces three different...
Solve the following linear programming problem using Solver. Be sure to write in your optimal solution...
Solve the following linear programming problem using Solver. Be
sure to write in your optimal solution below the problem. Max Z =
20X1 + 30X2 + 25X3 + 32X4 s.t. 4X1 + 8X2 + 5X3 + 6X4 ≤ 40 X1 + X2 ≥
3 (X1 + X2) ≤ (X3 + X4) ?1 ?2 ≥ 3 2 X1 = __________ X2 =
___________ X3 = ___________ X4 = ___________ Z = ____________
Solve the following linear programming problem using Solver. Be sure to write in your optimal solution...
Solve the following linear programming problem using Solver. Be
sure to write in your optimal solution below the problem.
Max Z = 20X1 + 30X2 + 25X3 + 32X4
s.t. 4X1 + 8X2 + 5X3 + 6X4 ≤ 40
X1 + X2 ≥ 3
(X1 + X2) ≤ (X3 + X4)
x1/x2 ≥ 3/2
X1 = __________X2 = ___________X3 = ___________X4 = ___________Z
= ____________
Consider the following transportation problem. Formulate this problem as a linear programming model and solve it...
Consider the following transportation problem. Formulate this
problem as a linear programming model and solve it using the MS
Excel Solver tool.
Shipment Costs ($), Supply, and
Demand:
Destinations
Sources
1
2
3
Supply
A
6
9
100
130
B
12
3
5
70
C
4
8
11
100
Demand
80
110
60
(4 points) Volume Shipped from Source A __________
(4 points) Volume Shipped from Source B __________
(4 points) Volume Shipped from Source C __________
(3 points) Minimum...
Use the method of this section to solve the linear programming problem. Minimize C = 2x...
Use the method of this section to solve the linear programming
problem.
Minimize
C = 2x −
3y + 6z
subject to
−x
+
2y
−
z
≤
9
x
−
2y
+
2z
≤
10
2x
+
4y
−
3z
≤
12
x ≥ 0, y ≥ 0,
z ≥ 0
The minimum is C =
at (x, y,
z) =
.
Use the simplex method to solve the linear programming problem. The maximum is ___ when x1=...
Use the simplex method to solve the linear programming problem.
The maximum is ___ when x1= ___ and x2=___
a.)
Maximize : z= 24x1+2x2
Subject to: 6x1+3x2<=10, x1+4x2<=3
With: x1>=0, x2>=0
b.)
Maximize: z=2x1+7x2
Subject to: 5x1+x2<=70, 7x1+2x2<=90, x1+x2<=80
With: x1,x2>=0
c.)
Maximize: z=x1+2x2+x3+5x4
Subject to: x1+3x2+x3+x4<=55, 4x+x2+3x3+x4<=109
With: x1>=0, x2>- 0, x3>=0, x4>=0
d.)
Maximize: z=4x1+7x2
Subject to: x1-4x2<=35 , 4x1-3x2<=21
With: x1>=0, x2>=0
Write the dual maximization problem, and then solve both the primal and dual problems with the...
Write the dual maximization problem, and then solve both the
primal and dual problems with the simplex method. (For the dual
problem, use x1, x2, and x3 as the variables and f as the
function.) Minimize g = 6y1 + 28y2 subject to 2y1 + y2 ≥ 14 y1 +
3y2 ≥ 14 y1 + 4y2 ≥ 17 . primal g = primal y1 = primal y2 = dual f
= dual x1 = dual x2 = dual x3 =
Use the simplex method to solve the linear programming problem. Maximize P = x + 2y...
Use the simplex method to solve the linear programming
problem.
Maximize
P = x + 2y + 3z
subject to
2x
+
y
+
z
≤
21
3x
+
2y
+
4z
≤
36
2x
+
5y
−
2z
≤
15
x ≥ 0, y ≥ 0, z ≥ 0
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