Problem $1.$

A still company estimates the demand for steel as follows $($in millions of tons per year$)$:

a$.(0\mathrm{.}3$ points$)$ If capacity is set at $18$ million tons, how much of a capacity cushion is there?

b$.(0\mathrm{.}2$ points$)$ What is the probability of idle capacity if capacity is set at $16$ million tons?

c$.(0\mathrm{.}5$ points$)$ If it costs $$8$ million per million tons of lost business and $$80$ million to build a million tons of capacity, which capacity level, among $10,12,14,16,$ and $18,$ will minimize the total costs?