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: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+150a) How many bags of popcorn must Diane sell to minimize her cost?b) What is Diane’s minimum cost?a) 10b) 50Step-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=150now [tex]x=-\frac{(-20)}{2(1)} \\x= 10[/tex]Hence to minimize her cost, she must sell a) x= 10 popcornsand her minimum cost isb) [tex]C(10)= (10)^{2} -20(10)+150\\C(10) = 100-200+150\\C(10) = 50[/tex]