Question

Solve the linear programming problem by the method of corners.

Maximize | P = 2x + 3y | ||||

subject to | x | + | y | ≤ | 10 |

3x | + | y | ≥ | 12 | |

−2x | + | 3y | ≥ | 11 | |

x ≥ 0, y ≥ 0 |

Answer #1

Solve the linear programming problem by the method of
corners.
Maximize P = 2x + 6y
subject to 2x + y ≤ 16
2x + 3y ≤ 24
y ≤ 6
x ≥ 0, y ≥ 0
The maximum is P = at (x, y) = .

Solve the linear programming problem by the method of corners.
Maximize P = 5x + 7y subject to 2x + y ≤ 16 2x + 3y ≤ 24 y ≤ 7 x ≥
0, y ≥ 0 The maximum is P = at (x, y) = .

Use the simplex method to solve the linear programming
problem.
Maximize
P = 4x + 3y
subject to
3x
+
4y
≤
30
x
+
y
≤
9
2x
+
y
≤
17
x ≥ 0, y ≥ 0

Use the simplex method to solve the linear programming
problem.
Maximize
P = 6x + 5y
subject to
3x
+
6y
≤
42
x
+
y
≤
8
2x
+
y
≤
12
x ≥ 0, y ≥ 0
The maximum is P =
at
(x, y) =

Solve the linear programming problem by the method of corners.
Find the minimum and maximum of
P = 3x + 2y subject to
3x + 5y ≥ 20
3x + y ≤ 16
−2x + y ≤ 4
x ≥ 0,
y ≥ 0.

Solve the linear programming problem by the method of corners.
Minimize C = 8x + 3y subject to x + y ≤ 48 x + 3y ≥ 60 9x + 5y ≤
320 x ≥ 10, y ≥ 0

Solve the linear programming problem by the method of
corners.
Find the minimum and maximum of P = 5x + 4y subject to
3x + 5y ≥ 32
3x + y ≤ 16
−2x + y ≤ 6
x ≥ 0, y ≥ 0
Minimum:
P =
x =
y =
Maximum:
P =
x =
y =

Use the simplex method to solve the linear programming
problem.
Maximize
P = x + 2y + 3z
subject to
2x
+
y
+
z
≤
14
3x
+
2y
+
4z
≤
24
2x
+
5y
−
2z
≤
10
x ≥ 0, y ≥ 0, z ≥ 0
The maximum is P =
at
(x, y, z) =
( )
.

2. Solve the linear programming problem by the simplex
method.
Maximize 40x + 30y subject to the constraints:
x+y≤5
−2x + 3y ≥ 12
x ≥ 0, y ≥ 0

Solve the linear programming problem by the method of corners.
Minimize C = 4x + 6y subject to 4x + y ≥ 38 2x + y ≥ 30 x + 3y ≥
30 x ≥ 0, y ≥ 0 The minimum is C = at (x, y) =

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