Question

Diane has a booth at the state fair that sells bags of popcorn she has found that her daily costs are approximated by the function c(x) =x squared -20x+150

Answer 1

Diane has a booth at the state fair that sells bags of popcorn she has found that her daily costs are approximated by the function c(x) =x squared -20x+150

a) How many bags of popcorn must Diane sell to minimize her cost?

b) What is Diane’s minimum cost?

a) 10

b) 50

Explanation:

According to the quadratic equation given in the question ,

`C(X)=x^(2) -20x+150`

the cost will be minimum at

`x= -(b)/(2a)`

comparing x^{2} -20x+150[/tex] with the standard quadratic equation
`ax^(2) +bx^(2) +c`

we get

a= 1, b = -20, c=150

now

`x=-((-20))/(2(1)) \\x= 10`

Hence to minimize her cost, she must sell

a) x= 10 popcorns

and her minimum cost is

b)
`C(10)= (10)^(2) -20(10)+150\\C(10) = 100-200+150\\C(10) = 50`