Question

a company sells eyeglasses. The company incurs a one-time fixed cost for $250,000. Each eyeglasses costs $140 to produce, and sells for $160.

a. Find the cost function, C, to produce x eyeglasses, in dollars.

b. Find the revenue function, R, from the sales of x eyeglasses, in dollars.

c. Find the break-even point, the point of intersection of the two graphs C and R.

d. What does the break even point mean?

e. Is this a lucrative way to earn money? explain.

Answer 1

one time fixed cost = $250,000

Selling price of one unit eyeglass =$160

Cost price of unit eyeglass = $140

a.

To produce x eyeglass

Fixed cost = $250,000

Cost price of x eyeglasses = x*Cost price of unit eyeglass = $140x

Total cost = C = $250,000 + $140x

b.

Revenue function

Total revenue generated on selling x eyeglasses = x*Selling price of unit eyeglass =R = $160x

c.

At break-even point

C = R

$250,000 + $140x = $160x

$20x = $250,000

x = 25,000/2 = 12,500

d.

At the point when the company has sold 12,500 eyeglasses it will reach a break even point which can be described as a point where there is no net profit or loss. ( Thus Revenue = Costs / Expenses)

e.

Yes it can be considered a lucrative way to earn money as the company on national level scale or global level can achieve selling 12500 eyeglasses soon then whatever they will selling would contribute to profits. Even though smaller number would have been better for the business model