Question

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.

Answer #1

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 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) =

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)=___________ .

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) = .

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 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.
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.
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 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) = .

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