Neptune Company has developed a small inflatable toy that it is anxious to introduce to its customers. The company$$s Marketing Department estimates that demand for the new toy will range between $18,000$ units and $38,000$ units per month. The new toy will sell for $$4\mathrm{.}00$ per unit. Enough capacity exists in the company$$s plant to produce $21,000$ units of the toy each month. Variable expenses to manufacture and sell one unit would be $$2\mathrm{.}00,$ and incremental fixed expenses associated with the toy would total $$27,000$ per month.

Neptune has also identified an outside supplier who could produce the toy for a price of $$2\mathrm{.}75$ per unit plus a fixed fee of $$20,000$ per month for any production volume up to $23,000$ units. For a production volume between $23,001$ and $43,000$ units the fixed fee would increase to a total of $$40,000$ per month.

Required:

$1.$ Calculate the break$-$even point in unit sales assuming that Neptune does not hire the outside supplier. $($Do not round your intermediate calculations.$)$

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

a$.$ It produces and sells $21,000$ units.

b$.$ It does not produce any units and instead outsources the production of $21,000$ 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 $21,000$ units that it sells and that it also commits to hiring the outside supplier to produce up to $17,000$ additional units.

$4.$ Assume that Neptune plans to use all of its production capacity to produce the first $21,000$ units that it sells and that it also commits to hiring the outside supplier to produce up to $17,000$ additional units.

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

b$.$ What total unit sales would Neptune need to achieve in order to attain a target profit of $$17,500$ per month?

c$.$ How much profit will Neptune earn if it sells $38,000$ units per month?

d$.$ How much profit will Neptune earn if it sells $38,000$ units per month and agrees to pay its marketing manager a bonus of $20$ cents for each unit sold above the break$-$even point from requirement $3?$

$5.$ If Neptune outsources all production to the outside supplier, how much profit will the company earn if it sells $38,000$ units?