canoeshasafixedcostof20,000.itcost40toproduceeachcanoe.thesellingpriceis80percanoe



canoeshasafixedcostof20,000.itcost40toproduceeachcanoe.thesellingpriceis80percanoe

Calculate the cost function C(x)
Our fixed cost is 20000.
Our variable cost is 40

The cost function is written as variable costs * number of units + fixed costs
C(x) = 40x + 20000.

Calculate the revenue function R(x)
The product sells for 80
Therefore, R(x) = 80x

Calculate the break-even point
Break-even is where C(x) = R(x)
40x + 20000. = 80x

Subtract 40x from each side of the equation:
40x + 20000. - 40x = 80x - 40x

Cancelling the 40x on the left side, we get:
40x = 20000.

Divide each side of the equation by 40
40x
40
=
20000.
40

Cancelling 40 on the left side, we get:
40x
40
=
20000.
40

x = 500 ← This is the break-even quantity.

Given the break even quantity x = 500, calculate the break even amount using the revenue function R(x)
R(500) = 80(500)
R(500) = 40000