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 $$80$ each. For the foreseeable future, sales volume should equal normal capacity of production.

Direct material $$590,000$

Direct labor $330,000$

Variable overhead $170,000$

Fixed overhead $($Note $1280,000$

Selling expense $($Note $2160,000$

Administrative expense $($fixed$)112,000$

$$1,642,000$

Notes:

$1.$ Beyond normal capacity, fixed overhead cost increases $$12,700$ 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 $$2\mathrm{.}40$ per unit.

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

Total cost $=$ $Answer

$+$ $Answer

X # of units.

b$.$ Prove your answer in requirement $($a$)$ relative to the total cost figure for $25,000$ units.

Total cost $=$ Fixed cost $+$ Variable cost

$=$

$+$

c$.$ Calculate the planned total cost at $20,000$ units. $Answer

d$.$ If Princeton were operating at normal capacity and accepted an order for $500$ more units, what would it have to charge for the order to earn a net income before income tax of $$16$ per unit on the new sale?

Required selling price $Answer

per unit