Question

Q8 Q22.) A company that manufactures small canoes has a fixed cost of $18,000. It costs $40 to produce each canoe. The selling price is $160 per canoe.​ (In solving this​ problem, let x represent the number of canoes produced and​ sold.)

Answer 1

The Cost function is the amount that each canoe costs, as well as the fixed cost.

let C(x) be the total amount
let x be the canoe produced

C(x) = 40x + 18000

The revenue function is the amount the canoe is selling at.

R(x) = 160x

160x = 40x + 18000

find what x is, subtract 40x from both sides

160x (-40x) = 40x (-40x) + 18000

160x - 40x = 18000

120x = 18000

isolate the x, divide 120 from both sides

120x/120 = 18000/120

x = 18000/120

R(x) = 150


I believe C means:
Break- even point: if it means the amount to make it back to $0.

Use "160x = 18000 + 40x" again.

x should still = 150, for after 150 canoes, they would make $0 profit.
A. the money coming in equals the money going out (for $0 profit)


hope this helps

Answer 2

A. fixed costs of 18,000 and then 40 per canoe

c(x) = 18000 +40x

B) sell price is 160 per canoe, so r(x) = 160x

C) break even, set both a and b equal to each other and solve for x

18000 + 40x = 160x

subtract 40x from each side:

1800 = 120x

divide both sides by 120
x = 18000 / 120 = 150 canoes

break even means the money coming in equals the money going out