Answer:
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
Step-by-step explanation:
According to the quadratic equation given in the question ,
[tex]C(X)=x^{2} -20x+150[/tex]
the cost will be minimum at
[tex]x= -\frac{b}{2a}[/tex]
comparing x^{2} -20x+150[/tex] with the standard quadratic equation [tex]ax^{2} +bx^{2} +c[/tex]
we get
a= 1, b = -20, c=150
now
[tex]x=-\frac{(-20)}{2(1)} \\x= 10[/tex]
Hence to minimize her cost, she must sell
a) x= 10 popcorns
and her minimum cost is
b) [tex]C(10)= (10)^{2} -20(10)+150\\C(10) = 100-200+150\\C(10) = 50[/tex]
