Question

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 + 0.3X + 0.27X2, where X is in megawatts. Revenue in dollars per hour from the sale of electricity is 15X−0.2X2. Find the value of X that gives maximum profit

Answer 1

$Cost = Y = 12 +0.3X+0.27X^2 \\ Revenue = R = 15X -0.2X^2 \\ Profit = R-Y \\ Π = 15X- 0.2X^2 -12 -0.3X -0.27X^2 \\ \frac{dΠ}{dX} = 15 -0.4X -0.3 -0.54X = 0 \\ 14.7 -0.94X = 0 \\ X = \frac{14.7}{0.94} = 15.64 \;megawatts$