Neptune Company has developed a small inflatable toy that it is anxious to introduce to its customers. The company's Marketing Department estimates that demand for the new toy will range between $10,000$ units and $30,000$ units per month. The new toy will sell for $$10\mathrm{.}00$ per unit. Enough capacity exists in the company's plant to produce $15,000$ units of the toy each month. Variable expenses to manufacture and sell one unit would be $$6\mathrm{.}00,$ and incremental fixed expenses associated with the toy would total $$34,000$ per month.

Neptune has also identified an outside supplier who could produce the toy for a price of $$5\mathrm{.}00$ per unit plus a fixed fee of $$27,000$ per month for any production volume up to $15,000$ units. For a production volume between $15,001$ and $35,000$ units the fixed fee would increase to a total of $$54,000$ per month.

Required:

Calculate the break$-$even point in unit sales assuming that Neptune does not hire the outside supplier.

Note: Do not round your intermediate calculations.

$2.$ How much profit will Neptune earn assuming:

a$.$ It produces and sells $15,000$ units.

b$.$ It does not produce any units and instead outsources the production of $15,000$ units to the outside supplier and then sells those units to its customers.

$3.$ Calculate the break$-$even point in unit sales assuming that Neptune plans to use all of its production capacity to produce the first $15,000$ units that it sells and that it also commits to hiring the outside supplier to produce up to $15,000$ additional units.

$4.$ Assume that Neptune plans to use all of its production capcity to produce the first $15,000$ units that it sells and that it also commits to hiring the outside supplier to produce up to $15,000$ additional units.

a$.$ What total unit sales would Neptune need to achieve in order to equal the profit earned in requirement $2a?$

b$.$ What total unit sales would Neptune need to achieve in order to attain a target profit of $$28,500$ per month?

c$.$ How much profit will Neptune earn if it sells $30,000$ units per month?

d$.$ How much profit will Neptune earn if it sells $30,000$ units per month and agrees to pay its marketing manager a bonus of $10$ cents for each unit sold above the break$-$even point from requirement $3?$