$(20$ points$)$ Assume that a decision is made to start ordering reactors at such a constant

rate per year from $1990$ until $2030,$ at which time orders will stop, so that all known

uranium reserves of $2\mathrm{.}3$ million metric tons will be used up

Assume:

$($a$)$ All plants are identical and need $150$ tons of natural uranium per year.

$($b$)$ It takes $10$ years to build a plant

$($c$)$ Every plant has a $30-$yr lifetime

$($d$)$ There are $120$ plants operating in $1990$

$($e$)$ Reactors operating in $1990$ start retiring in $2000,$ at a rate of $10/$yr$.$ For these reactors,

consider their needs only after $1990.$

Calculate how many reactors per year could be ordered and the maximum number of

reactors operating at any single time