$12\mathrm{.}8($Land$\text{'}$s End$)$ Geoff Gullo owns a small firm that manufactures $$Gullo Sunglasses.$$ He

has the opportunity to sell a particular seasonal model to Land$$s End. Geoff offers

Land$$s End two purchasing options:

This season's demand for this model will be normally distributed with mean of $200$ and

standard deviation of $125.$ Land's End will sell those sunglasses for $$100$ each. Geoff's

production cost is $$25.$

a$.$ How much would Land's End buy if they chose option $1?$

b$.$ How much would Land's End buy if they chose option $2$