Formulate the following problem. Note that this requires knowledge of the

optional content of section $6\mathrm{.}5\mathrm{.}1.$ In addition, the minimum order size of $50$

litres provides a further complication.

A company buys oil for heating. The supplier does not want to deal with

small orders, so there is a minimum order size of $50$ litres. The price per

litre is $$0\mathrm{.}90$ per litre for the first $200$ litres of an order, but each additional

litre in the same order costs only $$0\mathrm{.}75$ per litre.

We are now at $31$ October, with $300$ litres on hand. The expected number

of litres that they will need over the next seven months is:

November December January February March April May

$400600750820650350150$

All orders arrive on the first of every month. The capacity of the tank is

$1200$ litres. There is a charge of $$0\mathrm{.}05$ per litre per month; this charge is

based on the ending inventory in each month. They wish to have at least

$100$ litres on hand at the end of May