# Minimization Exercise on Nowledge College business administration studentExample of Linear Programming - Graphical Method

### Problem Data

We want to Minimize the following problem:

Objective Function
Z = 120X1 + 200X2
Subject to the following constraints

X1 + X2 = 65

X1 + 0X2 23

0X1 + X2 20

60X1 + 24X2 3000

X1, X2 ≥ 0

Description
Minimization Exercise on Nowledge College business administration studentA business student at Nowledge College must complete a total of 65 courses to graduate. The number of business courses must be greater than or equal to 23. The number of nonbusiness courses must be greater than or equal to 20. The average business course requires a textbook costing \$60 and 120 hours of study. Nonbusiness courses require a textbook costing \$24 and 200 hours of study. The student has \$3,000 to spend on books. What combination of business and nonbusiness courses minimizes total hours of study?

## 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: X1, X2 ≥ 0

The decision variables of the problem must comply with the non-negativityconstraint; 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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