Belli$-$Pitt, Inc produces a single product. The results of the company's operations for a typical month are summarized in contribution format as follows:

Sales $$540,000$

Less: variable expenses $360,000$

Contribution margin $180,000$

Less: fixed expenses $120,000$

Operating income $$60,000$

The company produced and sold $120,000$ kilograms of product during the month. There were no beginning or ending inventories.

Required:

a$)$ Given the present situation, compute

$1$ The break$-$even sales in kilograms.

$2$ The break$-$even sales in dollars.

$3$ The sales in kilograms that would be required to produce operating income of $$90,000.$

$4$ The margin of safety in dollars.

b$)$ An important part of processing is performed by a machine that is currently being leased for $$20,000$ per month. Belli$-$Pitt has been offered an arrangement whereby it would pay $$0\mathrm{.}10$ royalty per kilogram processed by the machine rather than the monthly lease.

$1$ Should the company choose the lease or the royalty plan?

$2$ Under the royalty plan, compute the break$-$even point in kilograms.

$3$ Under the royalty plan, compute the break$-$even point in dollars.

$4$ Under the royalty plan, determine the sales in kilograms that would be required to produce operating income of $$90,000.$