I need help on how to solve the programming problems below.

1. Solve the following integer programming problem. Provide only the values for A, B, and the Z. You may use any method you choose (graphical, enumeration of vertices, MS Solver, etc.)

Maximize Z = 120A + 80B

Subject to the constraints:
2A + 1B <= 6
7A + 8B <= 28
A >= 0 and integer
B >= 0 and integer

2. Formulate the following as a linear program. Do not solve it.

George developed two handcrafted items that he sells to shops. Although the demand for these items exceeds his capacity to produce them, George continues to work alone and limit his workweek to 50 hours per week. Item I takes 3.5 hours to produce and brings a profit of $28 while Item II takes 4 hours to produce and brings a profit of $31. How many items of each type should George produce weekly if his objective is to maximize total profit?

3. Solve the following linear program. Provide only the values for A, B, and the Z. You may use any method you choose (graphical, enumeration of vertices, MS Solver, etc.)

Maximize Z = 7A + 5B

Subject to the constraints:
4A + 3B <= 240
2A + 1B <= 100
A >= 0
B >= 0

Question: Suppose a linearprogramming (maximization) problem has been solved and the optimal value of the objective function is $300. Suppose an additional constraint is added to this problem. Explain how this might affect each of the following:
(a) The feasible region
(b) The optimal value of the objective function

Convert the following to a maximization problem.
Minimize: w = 2x + 3y + 5z
Subject to: x + y + z ≥ 5
X + y ≥ 7
2x + y + 3z ≥ 6
Do not need to solve. Just answer with the maximization problem.

What are the optimal values of x1, x2, and z?
Consider the following linearprogramming problem:
Max Z = $15x + $20y
Subject to : 8x + 5y 40
0.4x + y 4
x, y
Determine the values for x and y that will maximize revenue. Given this optimal revenue, what is the amount of slack associated with the first

Solve the following linearprogram using the graphical method:
Maximize Z = $9x1 + $15x2
Subject to: 3x2 ≤ 18
9x1 + 6x2 ≤ 54
x1, x2 ≥ 0.
See the attachment.

Using the linear approximation system to estimate the profit maximizing price requires that the managers know the costs of production and:
a. the production function
b. one price and quantity of demand
c. two prices and quantities of demand
d. decision-making process of the marketplace

39. Max Z = $0.30x + $0.90y
Subject to : 2x + 3.2y <= 160
4x + 2y <= 240
y <= 40
x, y >= 0.
Solve for the quantities of x and y which will maximize Z. What is the value of the slack variable associated with constraint 2?
45. Consider the following transportation problem:
1 2 Supply
1 5 6 100

Discuss the requirements of a linearprogramming (LP) model. Provide an example of an LP model and define each variable used. What are the key steps that need to be considered when formulating an LP problem?

A. Maximization Graph Solutions
Given the following maximizationlinearprogramming model, which of the possible solutions provided below is NOT feasible?
Maximize Z = 2X1 + 3X2
subject to:
4X1 + 3X2 < 480
3X1 + 6X2 < 600
a) X1 = 120 and X2 =0
b) X1 = 75 and X2 = 90
c) X1 = 90 and X2 = 75
d) X1 = 0 and X2 = 120
Ans