Question

Maximize p = 2x + 3y subject to 3x + 8y ≤ 30 6x + 4y ≤ 42 x ≥ 0, y ≥ 0.

Answer #1

Minimize C = −2x + 3y subject to 3x + 4y ≤ 24, 7x − 4y ≤ 16, and
x, y ≥ 0.

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

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) =

Consider the following linear programming problem.
Maximize
P = 3x + 9y
subject to the constraints
3x + 8y ≤ 1
4x − 5y ≤ 4
2x + 7y ≤ 6
x ≥ 0, y ≥ 0
Write the initial simplex tableau.
x
y
s1
s2
s3
P
Constant
1
4
6
0

Maximize objective function P=3x+4y
subject to: x + y ≤ 7 x ≥ 0
x+4y ≤ 16 y ≥ 0
Attach image from graphing calculator or draw your own graph, if
desired – must show feasible region and identify critical
(corner) points to receive full credit!

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 using the elimination method. Show all work.
3x – 2y = 1
4y = 6x – 2
Solve using the elimination method. Show all work.
x – 3y = -17
-x + 8y = 52

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) = .

Consider the following linear programming problem.
Maximize
P = 4x + 6y + 9z
subject to the constraints
2x
+
3y
+
z
≤
900
3x
+
y
+
z
≤
350
4x
+
2y
+
z
≤
400
x ≥ 0, y ≥ 0, z ≥ 0
Write the initial simplex tableau.
x
y
z
s1
s2
s3
P
Constant
900
350
400
0

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