Question

Use the method of corners to solve the linear programming problem. Find the maximum and minimum of Q = 5x + y subject to

5x + 2y ≥ 29

x + 2y ≥ 8

x + 4y ≤ 22

x ≥ 0, y ≥ 0.

The minimum is P = _________ at (x, y)=___________ .

The maximum is P = __________at (x, y)=___________ .

Answer #1

Use the method of corners to solve the linear programming
problem.
Find the maximum and minimum of
Q = 3x + y
subject to
5x
+
2y
≥
29
x
+
2y
≥
8
x
+
4y
≤
22
x ≥ 0, y ≥ 0.
The minimum is P = at
(x, y) =

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 =

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.
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) = .

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 simplex method.
Maximize
P = 5x + 4y
subject to
3x
+
5y
≤
214
4x
+
y
≤
172
x ≥ 0, y ≥ 0
The maximum is P =
at (x, y) = .

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) =

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

Use the method of this section to solve the linear programming
problem.
Minimize
C = x +
2y
subject to
4x
+
7y
≤
60
2x
+
y
=
28
x ≥ 0, y ≥ 0
The minimum is C =
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

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