Question

a company that manufactures small canoes has a fixed cost of $18,000. it costs $80 to produce each canoe. the selling price is $160 per canoe. (in solving this exercise let x represent the number of canoes produced and sold.) a. write the cost function. c(x)=18000 + 80x (type an expression using x as the variable.) b. write the revenue function. r(x)=160x (type an expression using x as the variable.) c. determine the break - even point. (225, 36000) (type an ordered pair. do not use commas in large numbers.) 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

Explanation:

Step1: Define break - even point concept

The break - even point is when revenue equals cost, i.e., $R(x)=C(x)$.

Step2: Recall cost and revenue functions

$C(x) = 18000 + 80x$ and $R(x)=160x$.

Step3: Set up the equation

$160x=18000 + 80x$.

Step4: Solve for x

Subtract $80x$ from both sides: $160x-80x=18000$, so $80x = 18000$. Then $x=\frac{18000}{80}=225$.

Step5: Find the revenue (or cost) at break - even

Substitute $x = 225$ into $R(x)$: $R(225)=160\times225 = 36000$.

Step6: Interpret break - even meaning

At the break - even point, the money coming in (revenue) equals the money going out (cost).

Answer:

B. the money coming in equals the money going out.