A summary of a manufacturing company's budgeted profit statement for its next financial year,when it expects to be operating at $75\%$ of capacity,is given below.

Sales $9,000$ at $$32$ $$288,000$

Less:

Direct materials $$54,000$

Direct wages $$72,000$

Production overhead: fixed $$42,000$

variable $$18,000$

total $$186,000$

Gross profit $$102,000$

Less: admin,selling and distribution costs: fixed $$36,000$

Varying with sales volume $$27,000$

total $$63,000$

Net profit $$39,000$

it has been estimated that:

if the selling price per unit were reduced to $$24,$the increased demand would utilize $90\%$ of the company's capacity without any additional advertising expenditure.

to attract sufficiet demand to utilize full capacity would require a $15\%$ reduction in the current selling price and a $$5,000$ special adversing campaingn.

$($a$)$ Calculate the breakeven point in units,based on the original budget.

$($b$)$ Calculate the profits and breakeven points which would result from each of the two alternatives and compare them with the original budget.