Respuesta :
Answer:
a) $825
b) $205.10
c) $47.5
d) R(51) = 872.5, R(52) = 920, R(53) = 967.5
Step-by-step explanation:
We are given the following information in the question:
[tex]R(x) = 0.006x^3 + 0.02x^2 + 0.5x[/tex]
where x is the number of lawn chairs.
a) Current daily revenue
[tex]R(50) = 0.006(50)^3 + 0.02(50)^2 + 0.5(50) = 825[/tex]
Thus, $825 is the current daily revenue when Pierce sells 50 lawn chairs daily.
b) Revenue increase if 54 lawn chairs were sold each day
[tex]R(54)-R(50)\\= 0.006(54)^3 + 0.02(54)^2 + 0.5(54) - 825\\= 205.10[/tex]
Thus, revenue increase $205.10 if 54 lawn chairs were sold each day.
c) Marginal revenue
[tex]R'(x) = \displaystyle\frac{dR}{dx} = \frac{d(0.006x^3 + 0.02x^2 + 0.5x)}{dx}\\\\R'(x) = 0.018x^2 + 0.04x+0.5\\R'(50) = 0.018(50)^2 + 0.04(50)+0.5 = 47.5[/tex]
Thus, $47.5 is the marginal revenue when 50 lawn chairs are sold daily.
d) R(51), R(52), and R(53)
[tex]R(51) = R(50) + 1R'(50) = 825 + 1(47.5) = 872.5\\R(52) = R(50) + 2R'(50) = 825 + 2(47.5) = 920\\R(53) = R(50) + 3R'(50) = 825 + 3(47.5) = 967.5[/tex]
