Question

A company that manufactures small canoes has a fixed cost of $ 18 comma 000$18,000. It costs $ 120$120 to produce each canoe. The selling price is $ 240$240 per canoe.​ (In solving this​ exercise, let x represent the number of canoes produced and​ sold.)a. Write the cost function.
​C(x)equals=
nothing ​ (Type an expression using x as the​ variable.)
b. Write the revenue function.
​R(x)equals=
nothing  ​(Type an expression using x as the​ variable.)
c. Determine the​ break-even point.

Answer 1

If the company makes 1 canoe only, then the cost is, the fixed cost plus how much it costs for the 1 canoe, or
180,000 + 1*120

if it makes 2 canoes
180,000 + 2*120
3 canoes   180,000 + 3*120
4canoes   180,000 + 4*120
x canoes  180,000 + x*120

so... we dunno what "x" is, but whatever "x" maybe, the cost ends up as 180,000 + x*120, or 180,000 + 120x

now, let's see the revenue
1 canoe 1 * 240
2 canoes 2*240
3 canoes 3*240
x canoes x*240

so.. whatever "x" maybe, the Revenue is x*240 or 240x

break-even point is when, the amount of expenses and earnings cancel each other out, or, there's no profit, but there's no loss either, same amount that's spent is also earned back

so, the break-even point occurs when Revenue = Cost

180,000 + 120x = 240x     <--- solve for "x"