posted by Yun Gao on .
The perfect pizza parlor estimates the average daily cost per pizza to be C(x) = (0.00025x^2 + 8x + 10)/x , where x is a number of pizzas made in a day.
a) determine the total cost at the level of production of 50 pizzas a day.
b) determine the production level that would minimize the average daily cost per pizza.
c) what is the minimum average daily cost per pizza?
cost per pizza at x = 50 is
[.00025(50)^2 + 8(50) +10 ]/50 = 8.21
* 50 = 410.63
dc/dx = [x (.0005 x + 8) -.00025x^2-8x-10) ]/x^2
when is the numerator zero?
.0005 x^2 + 8 x -.00025 x^2 -8 x -10 = 0
.00025 x^2 = 10
x = 200
for c, use 200 for x
(a) Plug in 50 for x and compute C(x).
(b) Solve for the value of x for which
C'(x) = dC(x)/dx = = 0.00025 x -20/x
25x^2 = 20,000
(c) Compute C(x) using the value of x from (b)