Let us say we have x, y and z hours put be the three types of laborers, I, II, III respectively

Thus we get x + y + z = 500 ------ ( 1 )

where 'z' has to be maximum

Also we are given the expenditure.

8x + 6y + 5z = 2800 ----- ( 2 )

From (1) we get x = 500 - y - z

Plugging it in equation (2), we get

8( 500 - y - z ) + 6y + 5z = 2800

4000 - 8y - 8z + 6y + 5z = 2800

2y + 3z = 1200

Since z has to be largest and total number of hours is 500 we try z = 300

That will give

y = 150

Plugging in these values in (1) we get x = 50.

We can verify that this solution which satisfies the given conditions