Question

A company that manufactures small canoes has a fixed cost of $20,000. It cost $40 to produce each canoe. The selling price is $80 per canoe. (In solving this exercise, let x represent the number of canoes produced and sold.)

1. Write the cost function.

2. Write the revenue function.

3. Determine the break-even point. Make sure your answer is an ordered pair.

4. This means that when the company produces and sells the break-even number of

canoes: a. there is less money coming in than going out b. the money coming in

equals the money going out c. there is more money coming in than going out d.

there is not enough information

Please explain how to work all of this out.

Answer 1

Answer:1) $40x 2)$80x 3) 500units 4)b

Explanation:

For the cost function, which is the amount used for production, we are told to use x and number of canoes produced, and canoe is produced at $40 per canoe, multiplying both

So production cost is $40x

And each canoe is sold at $80 per canoe, multiplying with no of canoes

so revenue is $80x

The break even cost happens when the amount of money put into the business equals the amount of revenue got, so total amount of money put into the business is the addition of the fixed cost and production cost of the canoes which is $20,000 + $40x (1)

And the revenue cost is 80x (2)

So equating (1) and (2) together, we find the value of x to reach the break even point

20000 + 40x = 80x

20000 = 80x - 40x

20000 = 40x

20000/40 = x

x = 500 units

I've already explained the answer to 4 being option b, because that's the fact we used to solve the amount of units to produce and sell to reach the break even point