# Linear Programming -Practice

- Author:
- Sangeeta Gulati

## Question:

An aeroplane can carry a maximum of 200 passengers. A profit of Rs 1000 is made on each executive class ticket and a profit of Rs 600 is made on each economy class ticket. The airline reserves at least 20 seats for executive class.However, at least 4 times as many passengers prefer to travel by economy class than by the executive class. Determine how many tickets of each type must be sold in order to maximise the profit for the airline. Formulate the LPP and find the maximum profit?

If x represents the number of executive class tickets and y represents the number of economy class tickets, what is the objective function?

## Constraint 1

Express an an inequality: "An aeroplane can carry a maximum of 200 passengers"

## Constraint 2

Express as an inequality: The airline reserves at least 20 seats for executive class

## Constraint 3

Express as an inequality: "at least 4 times as many passengers prefer to travel by economy class than by the executive class"

Write the non-negative restrictions:

## Plot the three constraints and non-negative restrictions.

## Corner Points

From the graph identify the feasible region and list the corner points. (Use point tool to mark the points of intersection, use Zoom tool to read the points carefully)

## Objective Function at Corner Points

Evaluate the value of Objective function at the corner points. Which point gives the maximum value?

## Conclusion:

For maximum profit the number of executive tickets to be sold are:

For maximum profit the number of economy tickets to be sold are:

The maximum profit is:

The maximum profit is: