In order to predict the cost per unit, c, of producing x units of her product, mary has developed the quadratic model

c(x) = 0.25x2 - 25x + 1425.

she now wants to use this function to estimate the minimum cost for making her product, and how many units will result in this minimum cost.

a. her first estimate is a minimum cost of $2000. explain why this is unreasonable.

b. next, mary guesses that if she produces no units her cost will be $0 per unit. explain why this is unreasonable.

c. finally, mary decides that she will be able to minimize her cost by producing as many units as possible. explain why this is unreasonable.