Question

Ms. Smith has decided to open a hot dog stand. She has found that her daily costs are approximated by the following equation: C(x) = x2 – 40x + 610. C(x) is the cost in dollars to sell x hot dogs.

a) Find the number of hot dogs she must sell to minimize her cost. ________

b) Find that minimum cost. _______________

c) What is Ms. Smith’s beginning cost each day for the hot dog stand? __________________

Answer 1

a.) To find the value of x to minimize C, we must differentiate the equation with respect with x and equate to 0.

dC(x) = 2x - 40 = 0
x = 20 hotdogs

b.) Substitute x = 20, to find the minimum cost

C = (20)^2 - 40(20) + 610
C = $ 210