A Colombian coffee shop sells its premium coffee at a constant rate of $280$ pounds per year. The coffee was purchased from a local supplier at a cost of $$2\mathrm{.}40$ per pound.

The The store estimates that the cost to place the order is $$45.$

The storage cost is $20\%$ annual interest.

$1\mathrm{.}1$ Determine the optimal amount of premium coffee to order.

$1\mathrm{.}2$ Determine the time between orders.

$1\mathrm{.}3$ Determine the total annual cost of maintaining this product $($including ordering cost$).$

$1\mathrm{.}4$ If the waiting time to receive the order is three weeks, determine the delivery point.

reorder.