word problems

Question

Sweet Candies, Inc has determine that when "x "candies are made daily, the average cost per candy is given by the formula C(x)=0.001x^2-0.14x+12.20

(a) What is the average cost per piece of candy if 30 pieces are made daily?

(b) How many candies should be made daily in order to minimize the average cost per candy? Please show all work. Thanks

Answer 1

a) Use 30 for x.

 

(.001 * (30^2)) - (0.14 * (30)) + 12.2

 

.001 * 900 - 4.2 + 12.2

 

.9 - 4.2 + 12.2 = -3.3 + 12.2 = 8.9

 

b)

 

Graph is a parabola pointing up.  The vertex of that parabola represents the minimum y value.

 

The x coordinate of the vertex is given by:

 

x = -b/(2a)

 

b = -0.14 and a = .001

 

x = -(-.14)/(2(.001)) = .14/.002 = 70

 

Plug in 70 to get the minimum cost.

 

.001(70^2) - .14(70) + 12.2

 

.001(4900) - 9.8 + 12.2

 

4.9 - 9.8 + 12.2

 

-4.9 + 12.2 = 7.3