Question

a company sells one of its product at Rs.12 per unit a year.its cost function is given by [c(x)=0.01x^2+8^x+7],where x represents the number of units.the number of units and the maximum profit for which profit function maximizes are:

Answer 1

profit = revenue - cost
= 12x - .01x^2 - 8^x - 7

d(profit)/dx = 12 - .02x - (8^x)(ln8)
= 0 for a max of profit

12 - .02x = ln8 (8^x)

if x = 0, LS = 12 , RS = ln8 or appr 2.08
if x = 1, LS = 11.98 , RS = appr 16

so there is a solution between 0 and 1

This question does not make much sense to me
the 8^x term in the cost function does not see right.
as x increases , the 8^x becomes huge.
Why would the cost increase at such a ridiculous rate as your production increases.

check the wording of the question.