An electric power plant uses solid waste for fuel in the production of electricity. The cost Y in dollars per hour to produce electricity is Y = 12+ .3x+.27x2, where x is in megawatts. Revenue in dollars per hour from the sale of electricity is 15x-.2x2. Find the value of X that gives maximum profit.

15.64 MW

Explanation:

The computation of value of X that gives maximum profit is shown below:-

Profit = Revenue - Cost

= 15x - 0.2x 2 - 12 - 0.3x - 0.27x 2

= 14.7x - .47x^2 - 12

After solving the above equation we will get maximum differentiate  for profit that is

14.7 - 0.94x = 0

So,

x = 15.64 MW

Therefore for computing the value of X that gives maximum profit we simply solve the above equation.