Question

An aeroplane can carry a maximum of 200 passengers a profit of rs 400 is made on each first class ticket

Answer 1

Let the first class air tickets and second class tickets sold be x and y

Now as the seating capacity of the aeroplane is 200,so x+y≤200

As 20 tickets for first class are to be reserved ,So we have x≥20

And as the number of tickets of second class should be at least 4 times that of first class y≥4x

Profit on sale of x tickets of first class and y tickets of second class Z=1000x+600y

Therefore LPP is (i.e) maximize Z=1000x+600y subject to constraints x+y≤200,x≥20,y≥4x and x,y≥0

Step 2:

Now let us plot the lines on the graph .

x=y=200,x=20 and y=4x

The region satisfying the inequalities x+y≤200,x≥20 and y≥4x is ABC and it is shown in the figure as the shaded portion.

Step 3:

Z=100x+600y

The corner points of the feasible region A(20,180),B(40,160),C(20,80)

The values of the objective function at these points are as follows:

At the Points (x,y) the value of the objective function subject to z=1000x+600y

At A(20,180),value of the objective function Z=1000x+600y⇒1000×20+600×180=20000+108000=128000

At A(40,160),value of the objective function Z=1000x+600y⇒1000×40+600×160=40000+96000=136000

At A(20,80),value of the objective function Z=1000x+600y⇒1000×20+600×80=20000+48000=68000

Step 4:

It is clear that at B(40,160) Z has the maximum value.

Hence x=40,y=160

This implies 40 tickets of first class and 160 of second class should be sold to get the maximum profit of Rs.136000.