Chapter $12,$ problem $13$

A mail$-$order house uses $18,000$ boxes a year. Carrying costs are $60$ cents per box a year, and ordering costs are $$96.$ The following price schedule applies.

Number of Boxes Price per Box

$1,000$ to $1,999$ $$1\mathrm{.}25$

$2,000$ to $4,9991\mathrm{.}20$

$5,000$ to $9,9991\mathrm{.}15$

$10,000$ or more $1\mathrm{.}10$

What is the lowest annual total cost of these boxes?