# Maximization Exercise The Really Big Shoe manufacturer of basketball and soccer sports shoesExample of Linear Programming - Graphical Method

### Problem Data

We want to Maximize the following problem:

- Objective Function
- Z = X
_{1}+ X_{2} - Subject to the following constraints
300000X

_{1}+ 1000000X_{2}≤ 30000000120X

_{1}+ 96X_{2}≤ 4000X

_{1}, X_{2}≥ 0- Description
**Maximization Exercise The Really Big Shoe manufacturer of basketball and soccer sports shoes**The Really Big Shoe is a manufacturing of basketball and football shoes. Ed Sullivan, the manager of marketing must decide the best way to spend advertising resources. Each football team sponsored requires 120 pairs of shoes. Each basketball team requires 32 pairs of shoes. Football coaches receive $ 300,000 for shoe sponsorship, and basketball coaches receive $ 1,000,000. Sullivan's promotional budget is $ 30,000,000. The Really Big Shoe has a limited supply (4 liters or 4000 cc) of flubber, a rare and costly compound used in athletic shoes. Each pair of basketball shoes requires 3 cc of flubber, and each pair of football shoes requires 1 ce. Sullivan wants to sponsor as many basketball and football teams as resources allow. Formulate the problem as a LP problem and solve the problem graphically.

## 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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