# Exercise to maximize profits for O’Connel AirlinesExample of Linear Programming - Graphical Method

### Problem Data

We want to Maximize the following problem:

- Objective Function
- Z = 2500X
_{1}+ 2000X_{2} - Subject to the following constraints
X

_{1}+ X_{2}≤ 1215X

_{1}+ 10X_{2}≤ 150X

_{1}+ 0X_{2}≤ 9X

_{1}, X_{2}≥ 0- Description
**Exercise to maximize profits for O’Connel Airlines**O’Connel Airlines is considering air service from its hub of operations in Cicely, Alaska, to Rome, Wisconsin, and Seattle, Washington. O’Connel has one gate at the Cicely Airport, which operates 12 hours per day. Each flight requires 1 hour of gate time. Each flight to Rome consumes 15 hours of pilot crew time and is expected to produce a profit of $2,500. Serving Seattle uses 10 hours of pilot crew time per flight and will result in a profit of $2,000 per flight. Pilot crew labor is limited to 150 hours per day. The market for service to Rome is limited to nine flights per day. Use the graphic method of linear programming to maximize profits for O’Connel Airlines.

## Solution

To solve the problem we will calculate the **feasible region** which is formed by the area satisfying the set of constraints.

Below we present the detailed calculations and graphs to solve the problem:

### Step 1:

**Non-negativity:** X_{1}, X_{2} ≥ 0

The decision variables of the problem must comply with the **non-negativity**constraint; that is, their values can be from 0 to plus.

In our graph, it means that the feasible region will be in the first quadrant:

**Note:** You can zoom the chart using the scroll wheel, as well as move the view by dragging it with the mouse.

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