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 Yequals=1010plus+0.60.6Xplus+0.230.23Upper X squaredX2​, where X is in megawatts. Revenue in dollars per hour from the sale of electricity is 1313Xminus−0.40.4Upper X squaredX2. Find the value of X that gives maximum profit

Answer 1

x = 31.24 MW

Step-by-step explanation:

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

As we know that

Profit = Revenue - Cost

= (13x - 0.4x^2) - (10 + 0.6x + 0.23x^2)

Now we simplify this equation which is as follows

= 13x - 0.4x^2 - 10 - 0.6x - 0.23x^2

= 12.4x - 0.63x^2 - 10

Now

12.4 - 0.3969x = 0

So, the x = 31.24 MW

Therefore for computing this we applied the above formula