Problem $19-02$

$5.$

The management of a firm wants to introduce a new product. The product will sell for $$5$ a unit and can be produced by either of two scales of operation. In the first, total costs are

$TC=$$$3,000+$$$2\mathrm{.}7Q.$

In the second scale of operation, total costs are

$TC=$$$4,020+$$$2\mathrm{.}4Q.$

a$.$ What is the break$-$even level of output for each scale of operation? Round your answers to the nearest whole number.

The first scale of operation: units

The second scale of operation: units

b$.$ What will be the firm's profits for each scale of operation if sales reach $3,400$ units? Round your answers to the nearest dollar.

The first scale of operation: $

The second scale of operation: $

c$.$ One$-$half of the fixed costs are noncash $($depreciation$).$ All other expenses are for cash. If sales are $1,000$ units, will cash receipts cover cash expenses for each scale of operation? Enter your answers as positive values. Round your answers to the nearest dollar.

The first scale of operation generates a ash flow of $

The second scale of operation generates a cash flow of $

d$.$ The anticipated levels of sales are the following:

$\backslash$table$[[$Year$,$Unit Sales$],[1,2,400],[2,3,400],[3,4,400],[4,5,400]]$

If management selects the scale of production with higher fixed cost, what can it expect in years $1$ and $2?$ Round your answers to the nearest dollar.

Earnings in year $1$: $

Earnings in year $2$: $

If the firm selects the scale with higher fixed costs, its earnings in year $1$ will be earnings in year $2.$

If sales reach only $3,400$ a year, was the correct scale of operation chosen? Be sure to consider all the factors.

should have been preferred.