Question

Leisure Enterprise’s total cost of producing speedboats is given by TC = 10 Q 3 – 4 Q 2 + 25 Q + 500. On the basis of this information, the marginal cost of producing the 25th speedboat is:

Answer 1

The marginal cost of producing the 25th speedboat is 18,575.

Step-by-step explanation:

Note that the given Leisure Enterprise’s total cost (TC) of producing speedboats is correctly stated as follows:

TC = 10Q^3 - 4Q^2 + 25^Q + 500 …….………….. (1)

Where Q represents the quantity of speedboats produced.

To obtain the marginal cost (MC) of producing speedboats, equation (1) is differentiated with respect to Q as follows:

MC = dTC/dQ = 30Q^2 - 8Q + 25 ………………… (2)

Finding the marginal cost (MC) of producing the 25th speedboat implies that Q = 25.

Substituting Q = 25 into equation (2), we have:

MC = (30 * 25^2) - (8 * 25) + 25 = 18,575

Therefore, the marginal cost of producing the 25th speedboat is 18,575.