Pierce Manufacturing determines that the daily revenue, in dollars, from the sale of x lawn chairs is . Currently, Pierce sells 50 lawn chairs daily.
a) What is the current daily revenue?
b) How much would revenue increase if 55 lawn chairs were sold each day?
c) What is the marginal revenue when 50 lawn chairs are sold daily?
d) Use the answer from part (c) to estimate R(51), R(52), and R(53).

The correct answers are a) $652.5; b) $212.375; c) $13.05; d) R(51) = $689.52, R(52) = $732.68, R(53) = $775.125.

Step-by-step explanation:

Revenue function of Pierce Manufacturing from the sale of x lawns is given by R(x) = 0.005 + 0.01 + 0.05x.

Daily, Pierce Manufacturing is selling 50 lawn chairs.

a) Current daily revenue, i.e. x is 50 = 625 + 25 + 2.5 = $ 652.5.

b) Increase in revenue by selling 5 more chairs = R(55) - R(50) = $ (864.875 - 652.50) = $ 212.375.

c) Marginal Revenue function is given by dividing the revenue function by quantity. Therefore MR(x) = 0.005 + 0.01x + 0.05.

Value MR(50) = 12.5 + 0.5 + 0.05 = $ 13.05.

d) The value of R(51) = MR(51) × 51 = $ (13.52 × 51) = $ 689.52.

The value of R(52) = MR(52) × 52 = $ (14.09 × 52) = $ 732.68.

The value of R(53) = MR(53) × 53 = $ (14.625 × 53) = $ 775.125.