Find the values of the function on the given feasible region

Find the value(s) of the function on the given feasible region. Find the maximum and minimum of z = 7x + 9y.

z=7x+9y is positive for any x and y as x and y lie in first quadrant.

To find maximum consider the two parallel lines(1.joining (0,4) and (6,0) 2.joining (5/2,5) and (10,0))

At points on line 2,z will have maximum as- for any y , x is greater in line 2 than in 1.And now on line two x is highest at (10,0).

So at (10,0) z will have maximum,implies z=70.

Similarly

To find minimum consider the two parallel lines(1.joining (0,4) and (6,0) 2.joining (5/2,5) and (10,0))

At points on line 1,z will have minimum as- for any y , x is lesser in line 1 than in 2.And now on line 1, x is lowest at (0,4).

So at (0,4) z will have minimum,implies z=36.

Hence answer is option A.