Question

A company that manufacturers canoes has a fixed cost of $18,000. It cost $20 to produce each canoe. The selling price per canoe is $80. Let x be the number of canoes produced and sold. What is the cost function? What is the revenue function? What is the break-even point?

Answer 1

a) They ask to the cost function, and we know that there is a fixed cost of 18000 and that each canoe cost 20 to produce it, then we can write it mathematically as:

$c(x)=20x+18000$

b) The revenue function is given by the selling price, which is 80, and the number of canoes sold, then we can write it mathematically as:

$r(x)=80x$

c) the break-even point is given when the revenues cover the costs, then is the intersection point of the two functions:

$20x+18000=80x$$60x=18000$$x=300$

And we can replace it to find the other component:

$y=80x=80\ast300=24000$

So we can conclude that the break-even point is when is sold 300 canoes and the costs and the revenues are the same, that is $24000