Question

A company manufactures and sells blank audiocassette tapes. The weekly fixed cost is ​$10,000 and it costs ​$0.40 to produce each tape. The selling price is ​$2 per tape. How many tapes must be produced and sold each week for the company to have a profit?

Answer 1

6251 tapes

Step-by-step explanation:

Given: fixed cost is ​$10,000.

Variable cost is $0.40 to produce each tape.

Selling price is $2 per tape.

Lets assume number of tapes to be produced and sold be "x"

We know, Total cost=
`Fixed\ cost+ Variable\ cost`

∴ Total cost=
`10000+ 0.40* x`

Total cost=
`10000+0.40x`

As given, selling price is $2 per tape.

∴ For attaining break even point, Tota cost = Selling price.

`10000+0.40x= 2x`

Solving the equation to find the value of x

⇒
`10000+0.40x= 2x`

Subtracting both side by 0.4x

⇒
`10000= 1.60x`

Dividing both side by 1.60

⇒
`x= (10000)/(1.60)`

∴ x= 6250

Hence, number of tapes must be sold and purchased is 6250 to attain break even in the business, however selling one more tapes will get profit is 6251.