Step 1:

It is given that the normal speed of the motorcycle is $50km/hr$

His increased speed is 80km/hr

he has at most of 1hour's time.

Let $x$ and $y$ be the time,which we takes,when the speed is normal

$\therefore 80x+50y\leq 4000$

$\Rightarrow 8x+5y\leq 400$

The cost for the petrol when goes in the normal speed is Rs.2 per kms.

The cost for the petrol when goes in the increased speed is Rs.3 per kms.

He has at most of Rs 120 to spend.

Step 2:

Therefore $2x+3y\leq 120$

$x\geq 0,y\geq 0$

The objective function is $Z=x+y$ subjected to the constraints $8x+5y\leq 400,2x+3y\leq 120,x,y\geq 0$

$Z=x+y$ subjected to constraints $8x+5y\leq 400,2x+3y\leq 120$