Princeton Manufacturing Company summarizes the following total cost data for the month of March. Princeton has a normal capacity per month of $25,000$ units of product that sell for $$20$ each. For the foreseeable future, sales volume should equal normal capacity of production.

Direct material $$147,500$

Direct labor $82,500$

Variable overhead $42,500$

Fixed overhead $($Note $170,000$

Selling expense $($Note $240,000$

Administrative expense $($fixed$)28,000$

$$410,500$

Notes:

$1.$ Beyond normal capacity, fixed overhead cost increases $$3,175$ for each $1,000$ units or fraction thereof until a maximum capacity of $30,000$ units is reached.

$2.$ Selling expenses are a $5\%$ sales commission plus shipping costs of $$0\mathrm{.}60$ per unit.

a$.$ Using the information available, prepare a formula to estimate Princeton's total cost at various production volumes up to normal capacity.