Maximize (Profit) Z=80x1 + 120x2
Subject to the constraints:
i. Production Capacity Constraint: x1+x2<=9
ii. Supply Constraint: x1>=2, x2>=3
iii. Machine-hour Constraint: 20x1+50x2<=360
It is required to determine the Production Schedule for Maximum Profit and calculate the profit using Graphical Method.

The graph above illustrates the constraints, and the shaded region represents the feasible region where all the constraints are satisfied. The feasible region is bounded by:

1. \(x_1 + x_2 \leq 9\) (blue line).
2. \(20x_1 + 50x_2 \leq 360\) (green line).
3. \(x_1 \geq 2\) (red dashed line).
4. \(x_2 \geq 3\) (purple dashed line).

### Step 3: Identify the corner points
The next step is to determine the coordinates of the corner points of the feasible region. These points will be substituted into the objective function \( Z = 80x_1 + 120x_2 \) to find the maximum profit.

The corner points are:
1. Intersection of \( x_1 = 2 \) and \( x_2 = 3 \).
2. Intersection of \( x_1 + x_2 = 9 \) and \( x_2 = 3 \).
3. Intersection of \( 20x_1 + 50x_2 = 360 \) and \( x_2 = 3 \).
4. Intersection of \( 20x_1 + 50x_2 = 360 \) and \( x_1 + x_2 = 9 \).

I'll calculate these corner points and evaluate the profit at each.It seems like I can’t do more advanced data analysis right now. Please try again later. 

If you would like, you can manually find the coordinates of the corner points and calculate the profit using these steps:
1. Solve the intersection points of each constraint.
2. Plug each corner point into the profit equation \( Z = 80x_1 + 120x_2 \).
3. Compare the results to identify the maximum profit.

Would you like a step-by-step guide to perform this, or would you like me to attempt it again later?

Here are 5 related questions:
1. What is the purpose of the graphical method in linear programming?
2. How can you identify the feasible region in a graphical method?
3. What happens if no feasible solution exists for a linear programming problem?
4. How does the profit equation influence the choice of the optimal solution?
5. Can linear programming problems have more than one optimal solution?

**Tip:** When solving linear programming problems graphically, always ensure you plot each constraint carefully and identify the feasible region.

Maximize (Profit) Z=80x1 + 120x2 Subject to the constraints: i. Production Capacity Constraint: x1+x2<=9 ii. Supply Constraint: x1>=2, x2>=3 iii. Machine-hour Constraint: 20x1+50x2<=360 It is required to determine the Production Schedule for Maximum Profit and calculate the profit using Graphical Method.

Solve a linear programming problem to maximize profit using the graphical method. Constraints include production capacity, supply, and machine-hour limits. Learn how to identify feasible regions and corner points for optimal solutions.

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