Pierce Manufacturing determines that the daily revenue, in dollars, from the sale of x lawn chairs is R(x)=0.005x^3 + 0.01x^2 + 0.5x. Currently, Pierce sells 70 lawn chairs daily. Determine: (a) What is the current daily revenue? (b) What is the marginal daily revenue when x = 70?
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To find the current daily revenue, we need to substitute x = 70 into the revenue function R(x).
a) R(x) = 0.005x^3 + 0.01x^2 + 0.5x
R(70) = 0.005(70)^3 + 0.01(70)^2 + 0.5(70)
Using a calculator, we can calculate the value of R(70) to be:
R(70) ≈ $244.5
Therefore, the current daily revenue is approximately $244.5.
b) To find the marginal daily revenue when x = 70, we need to find the derivative of the revenue function R(x) with respect to x.
R'(x) = d/dx (0.005x^3 + 0.01x^2 + 0.5x)
R'(x) = 0.015x^2 + 0.02x + 0.5
Now, we substitute x = 70 into the derivative function R'(x):
R'(70) = 0.015(70)^2 + 0.02(70) + 0.5
Using a calculator, we can calculate the value of R'(70) to be:
R'(70) ≈ $105.5
Therefore, the marginal daily revenue when x = 70 is approximately $105.5.
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