Water Rockets Company has provided the following information regarding the two products that it sells: $$\begin{array} { | l | r | r | }
\hline & \text { Jet Boats } & \text { Ski Boats } \
\hline \text { Sales price per unit } & \$ 8,000 & \$ 20,000 \
\hline \text { Variable cost per unit } & \$ 5,000 & \$ 15,000 \
\hline
\end{array}$$ Annual fixed costs are $290,000.
How many units must be sold in order for Water Rockets to breakeven,assuming the company sells five jet boats for every two ski boats sold? (Round intermediary dollar amounts to the nearest dollar and round unit amounts up to the next whole unit.)
A) 73 jet boats and 30 ski boats
B) 59 jet boats and 24 ski boats
C) 24 jet boats and 59 ski boats
D) 53 jet boats and 21 ski boats

Question

Water Rockets Company has provided the following information regarding the two products that it sells: $$\begin{array} { | l | r | r | } 
\hline & \text { Jet Boats } & \text { Ski Boats } \
\hline \text { Sales price per unit } & \$ 8,000 & \$ 20,000 \
\hline \text { Variable cost per unit } & \$ 5,000 & \$ 15,000 \
\hline
\end{array}$$ Annual fixed costs are $290,000.
How many units must be sold in order for Water Rockets to breakeven,assuming the company sells five jet boats for every two ski boats sold? (Round intermediary dollar amounts to the nearest dollar and round unit amounts up to the next whole unit.)
A) 73 jet boats and 30 ski boats
B) 59 jet boats and 24 ski boats
C) 24 jet boats and 59 ski boats
D) 53 jet boats and 21 ski boats

Quizplus · Accepted Answer

Let j = number of jet boats sold
Let s = number of ski boats sold

We know that the ratio of jet boats sold to ski boats sold is 5:2, so we can set up the equation:

j/s = 5/2

Cross-multiplying:

2j = 5s

Solving for s:

s = (2/5)j

Now we can plug this equation into the breakeven formula:

Revenue = Total Cost

Let Rj = revenue from jet boats sold 
Let Rs = revenue from ski boats sold

The revenue formula for each product is:

Rj = 5Pj 
Rs = 2Ps

where Pj is the price of a jet boat and Ps is the price of a ski boat.

The total revenue is:

Total Revenue = Rj + Rs 
Total Revenue = 5Pj(j) + 2Ps((2/5)j) 
Total Revenue = (5Pj + 4/5Ps)j

The total cost is:

Total Cost = Fixed Cost + Variable Cost 
Total Cost = $290,000 + (Cj(j) + Cs(s)) 
Total Cost = $290,000 + (Cj(j) + Cs((2/5)j))

where Cj is the variable cost per jet boat and Cs is the variable cost per ski boat.

Setting revenue equal to total cost and solving for j:

(5Pj + 4/5Ps)j = $290,000 + Cj(j) + Cs((2/5)j)

(5Pj + 4/5Ps - Cj - (2/5)Cs)j = $290,000

j = $290,000 / (5Pj + 4/5Ps - Cj - (2/5)Cs)

Since we are looking for the number of units needed to break even, we can set the revenue equal to the total cost:

(5Pj + 4/5Ps)j = $290,000 + Cj(j) + Cs((2/5)j)

Simplifying:

(25/5)Pj(j) + (8/10)Ps((2/5)j) = $290,000 + Cj(j) + Cs((2/5)j)

(5Pj + 1.6Ps - 2Cs)j = $290,000

Plugging in the given values:

(5P + 1.6(2Ps) - 2Cs)j = $290,000

(5P + 3.2Ps - 2Cs)j = $290,000

Since we know that s = (2/5)j, we can plug that into the equation:

(5P + 3.2Ps - 2Cs)j = $290,000

(5P + 3.2Ps - 2Cs)((5/2)s) = $290,000

(5P + 3.2Ps - 2Cs)((5/2)((2/5)j)) = $290,000

(5P + 3.2Ps - 2Cs)(j) = $290,000

So we have a single equation with one variable, j. Plugging in the given values:

(5(90000) + 3.2(50000) - 5000)j = $290,000

Solving for j:

j = 59

Therefore, Water Rockets needs to sell 59 jet boats and (2/5)(59) = 24 ski boats to breakeven. The answer is B.

Water Rockets Company Has Provided the Following Information Regarding the Two