Question

suppose the total cost of a certain commodity is given by 𝐶(𝑥) = 1/10 𝑥^2 +

       6𝑥 + 50 dollars with selling price 𝑝(𝑥) = 70 − ' x/ 2 dollars per item.

 a) What is the actual cost of producing the 40th unit?

b) Use marginal cost to estimate the cost of producing the 40th unit.

c) What is the actual revenue derived from the sale of the 25th unit.

d) Use the marginal revenue to estimate the revenue derived from the sale of the 25th unit.

Answer 1

a) The actual cost of producing the 40th unit is:

C(40) = 1/10×40²+ 6×40 + 50 = 450.

b) The marginal cost of producing the 40th unit is:

MC(40) = C'(40) = 2/10×40 + 6 = 14.

c) What is the actual revenue derived from the sale of the 25th unit is:

TR(25) = p(x)×x = 70×25 - 25²/2 = 1,437.5.

d) The marginal revenue derived from the sale of the 25th unit is:

MR(25) = TR'(25) = 70 - 25 = 45.