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 $20,000$ units and $35,000$ units per month. The new toy will sell for $$9\mathrm{.}00$ per unit. Enough capacity exists in the company's plant to produce $25,000$ units of the toy each month. Variable expenses to manufacture and sell one unit would be $$5\mathrm{.}00,$ and incremental fixed expenses associated with the toy would total $$30,000$ per month.

Neptune has also identified an outside supplier who could produce the toy for a price of $$4\mathrm{.}00$ per unit plus a fixed fee of $$71,000$ per month for any production volume up to $25,000$ units. For a production volume between $25,001$ and $55,000$ units the fixed fee would increase to a total of $$142,000$ 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.

How much profit will Neptune earn assuming:

a$.$ It produces and sells $25,000$ units.

b$.$ It does not produce any units and instead outsources the production of $25,000$ units to the outside supplier and then sells those units to its customers.

Calculate the break$-$even point in unit sales assuming that Neptune plans to use all of its production capacity to produce the first $25,000$ units that it sells and that it also commits to hiring the outside supplier to produce up to $10,000$ additional units.

Assume that Neptune plans to use all of its production capacity to produce the first $25,000$ units that it sells and that it also commits to hiring the outside supplier to produce up to $10,000$ 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 $$72,500$ per month?

c$.$ How much profit will Neptune earn if it sells $35,000$ units per month?

d$.$ How much profit will Neptune earn if it sells $35,000$ 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 $3?$

If Neptune outsources all production to the outside supplier, how much profit will the company earn if it sells $35,000$ units?

$\backslash$table$[[1.$ Break$-$even point in unit sales $-$ without hiring,$7,500,$units$],[2$a$.$ Profit if produces and sells,$$0,000,],[2$b$.$ Profit if outsources production and sells,,$],[3.$ Break$-$even point in unit sales $-$ hiring,,units$],[4$a$.$ Total unit sales,,units$],[4$b$.$ Total unit sales to achieve a target Profit of $$72,500,,$units$],[4$c$.$ Net operating income,,$],[4$d$.$ Net operating income $-$ bonus to marketing manager,,$]]$M