Question

An electronics company is planning to manufacture a new line of​ high-end noise reduction ear buds. Fixed costs will be ​$122 comma 200 and it will cost ​$12 to produce each pair of ear buds. The ear buds will sell for ​$38 a pair. Using the equations for cost C and revenue R as given below where x represents the units of​ product, find the​ break-even point for producing the new ear buds. C(x) = fixed cost + (cost per unit produced) multiplied by xR(x) = (price per unit sold) multiplied by xWhat is the break-even point? (Type an ordered pair, but do not use commas in any individual coordinates.)

Answer 1

4700 pairs

Explanation:

Fixed cost = $122,200

Cost of producing 1 pair = $12

Let x be the no. of pairs

So, Cost of producing x pairs = 12 x

Total cost C(x) = 122200+12x

Selling price of 1 pair = $38

Selling price of x pairs R(x)= 38x

Now we are supposed to find the​ break-even point for producing the new ear buds.

So, C(x)=R(x)

So,
`122200+12x = 38 x`

`122200= 38 x- 12 x`

`122200= 26 x`

`(122200)/(26)=x`

`4700=x`

Hence the break even point is producing 4700 pairs