Let x₁, x₂, and x₃ represent number of units of product A, B, and C and the constraints represent the availability of materials 1, 2, and 3.

Given this LP model

Maximize Z = $100x₁ + $60x₂ + $50x₃ (Profit)

Subject to

2x₁ + 3x₂ + 4x₃ 30 (Material 1)

x₁ + 3x₂ + 2x₃ 22 (Material 2)

6x₁ + 3x₂ + 4x₃ 30 (Material 3)

x₁, x₂, x₃ 0

The sensitivity report for this problem above is provided below as Excel Solver output. You will need this output to answer (a) through (g) below each part of which is to be considered independently of all others.

What is the optimal profit? Show your work. (2 points)

Determine the range of optimality for the objective function coefficient of the decision variable x2. (2 points)

If the profit contribution of product A decreased to $75/unit. Without resolving the entire problem, decide if the optimal solutions and the value of the objective function can be determined (if yes, then provide the optimal values). (4 points)

What will be the impact on the profit when we force the production of 2 units of Product C (i.e. x₃= 2)? If you can determine what the new optimal value of the objective function is, then do so. If you cannot determine the new optimal value of the objective function, explain why. (3 points)

Some values in the Sensitivity report were deleted by your professor. Complete the LP table below: Write the corresponding value of each item deleted in the Sensitivity report and provide a brief justification for your answer. (8 points: 2 points each)

Number	Item	Value	Brief Justification
1	AI
2	AD		.
3	SP
4	SAD

The Manager is considering increasing Material 2 and Material 3 values by 2 units EACH. Without resolving the entire problem, decide if the impact of the changes on the optimal solutions and the value of the objective function can be determined (if yes, then provide the optimal values). Show your work. (6 points)

If one additional unit of the third resource (i.e. Material 3 constraint) could be obtained/purchased at a premium of $6, what impact would this have on profit? If you can determine what the new optimal value of the objective function is, then do so. If you cannot determine the new optimal value of the objective function, explain why. (3 points)