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=11+0.4X+0.29X2, where X is in megawatts. Revenue in dollars per hour from the sale of electricity is 16X−0.2X2. Find the value of X that gives maximum profit. (Round to two decimal places.)

Answer 1

The value of X that gives maximum profit is 15.92.

Step-by-step explanation:

Before answering the question, Y and Revenue (R) given in the question are first correctly restated as follows:

Cost = Y = 11 + 0.4X + 0.29X^2 .......................................... (1)

Revenue = R = 16X − 0.2X^2 .............................................. (2)

Differentiating each of equations (1) and (2) with respect to X to obtain marginal cost (MC) and marginal revenue (MR), we have:

dY/dX = MC = 0.4 + 0.58X .................................................. (4)

dR/dX = MR = 16 - 0.4X ....................................................... (5)

In production theory, profit is maximized when MR = MC. Therefore, we equate equations (4) and (5) and solve for X as follows:

0.4 + 0.58X = 16 - 0.4X

0.58X + 0.4X = 16 - 0.4

0.98X = 15.6

X = 15.6 / 0.98

X = 15.92

Therefore, the value of X that gives maximum profit is 15.92.