Question
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?
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?
Answers
Damon
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
[.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
drwls
(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
= 0
25x^2 = 20,000
(c) Compute C(x) using the value of x from (b)
(b) Solve for the value of x for which
C'(x) = dC(x)/dx = = 0.00025 x -20/x
= 0
25x^2 = 20,000
(c) Compute C(x) using the value of x from (b)
Yun Gao
thanks :)