Consider periodic shipments between two cities that are $475$ miles apart by road. Serving a yearly demand of $120$ tons

of a product with a unit weight $=20lb$ and volume $=\frac{1}{f}{t}^3,$ answer the questions below regarding total logistics costs

$($TLC$).$ Production and consumption happen at constant rates, each ton of the product is valued at $$5,000\mathrm{.}00,$ and the

inventory carrying rate was estimated to be $25\%$ of the product's value. Consider a PPI ${?}_{}=155.$

A$)$ What is the maximum payload of a truck trailer used in this series of periodic shipments? Consider a weight capacity of $25$

tons and a cube capacity of $2,750f{t}^3.$

B$)$ If you ship only full truckloads, what is the resulting TLC Fr for the year?

C$)$ If shipments must happen exactly once a month, what is the resulting $TL{C}_{}$ for the year?

D$)$ If you ship the cost$-$minimizing payload, what is the resulting $TL{C}_{}$ for the year?