Cheryl Montoya picked up the phone and called her boss, Wes Chan, the vice president of marketing at Piedmont Fasteners Corporation: $$Wes$,$ I$$m not sure how to go about answering the questions that came up at the meeting with the president yesterday.$$

"What's the problem?"

$$The president wanted to know the break$-$even point for each of the company$$s products, but I am having trouble figuring them out.$$

$$I$$m sure you can handle it$,$ Cheryl. And, by the way, I need your analysis on my desk tomorrow morning at $8$:$00$ sharp in time for the follow$-$up meeting at $9$:$00.$

Piedmont Fasteners Corporation makes three different clothing fasteners in its manufacturing facility in North Carolina. Data concerning these products appear below:

Velcro Metal Nylon

Annual sales volume $104,000208,000302,000$

Unit selling price $ $2\mathrm{.}20$ $ $1\mathrm{.}60$ $ $1\mathrm{.}50$

Variable expense per unit $ $1\mathrm{.}00$ $ $0\mathrm{.}80$ $ $1\mathrm{.}10$

Total fixed expenses are $$262,000$ per year.

All three products are sold in highly competitive markets, so the company is unable to raise prices without losing an unacceptable numbers of customers.

The company has an extremely effective lean production system, so there are no beginning or ending work in process or finished goods inventories.

Required:

$1.$ What is the company$$s overall break$-$even point in dollar sales?

$2.$ Of the total fixed expenses of $$262,000,$ $$27,000$ could be avoided if the Velcro product is dropped, $$129,600$ if the Metal product is dropped, and $$78,400$ if the Nylon product is dropped. The remaining fixed expenses of $$27,000$ consist of common fixed expenses such as administrative salaries and rent on the factory building that could be avoided only by going out of business entirely.

a$.$ What is the break$-$even point in unit sales for each product?

b$.$ If the company sells exactly the break$-$even quantity of each product, what will be the overall profit of the company?