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# Linear Program Maximization Problems

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

\$2.19