Marginal Revenue/profit question

Question

If marginal revenue is -0.009x^2 + 1020 and the cost per unit is 1.5, how much do profits increase by when output is expanded from 90 units to 148 units?

Answer 1

MR=-.009x^2+1020 AC=1.5=MC, TC=1.5x

TR= -.003x^3 +1020x + k where k= an unknown constant

Profit = TR-TC = -.003x^3 +1018.5x + k

for x = 90 to 148

Profit changes from -.003(90)^2 + 1018.5(90) + k to -.003(148)^2 +1018.5(148) + k

-.003(8100) = -24.3

1018(90) = 91620

-.003(21904) = -65.712

1018.5(148) = 150738

profit increased by 150738-91620 -65.712 + 24.3

= 59,076.588