$2.(12$ points$)$ Perkins Company produces and sells a single product. The company's income statement for the most recent month is given below:

Sales $(15,000$ units at $$29$ per unit$)$

$$435,000$

Less variable costs:

Direct materials $($variable$)$

Direct labor $($variable$)$ $$60,000$

Variable factory overhead

$75,000$

Variable selling and other expenses..

Contribution margin

Less fixed expenses:

Fixed factory overhead

$100,000$

Fixed selling and other expenses

$85,000$

Net operating income

$45,000$

$30,000,\frac{210,000}{225,000}$

$\frac{185,000}{\text{\$}40\mathrm{.}000}$

There are no beginning or ending inventories.

Required:

a$.$ Compute the company's break$-$even point in units and sales dollars.

b$.$ What would the company's monthly net operating income be if sales and total variable costs increased by $32\%$ and total fixed factory overhead dropped by $$41,000?$

c$.$ What total level of sales $($in units$)$ must the company achieve in order. to earn a target profit of $$72,000?$

d$.$ The company has decided to automate a portion of its operations. The change will reduce direct labor costs per unit by $60\%,$ but it will double the costs for fixed factory overhead. Every other cost remains unchanged. Compute the new break$-$even point in units.