Get-Aways Company sells sightseeing tours of the Ottawa Valley for $3229 per person. Overhead expenses for the company are 11% of Cost and the target profit is 12% of cost. What is the lowest price they can offer while still covering all of the costs and expenses?

Let's determine the lowest price Get-Aways Company can offer while covering all costs and overheads, given the overhead expenses are 11% of cost, and the target profit is 12% of cost.

1. **Let "C" represent the cost** of providing the tour for one person.
2. The overhead is 11% of the cost, so the overhead is $0.11C$.
3. The target profit is 12% of the cost, so the profit is $0.12C$.

The total price charged should cover the cost, overhead, and profit, so the price equation becomes:
\[
\text{Price} = C + 0.11C + 0.12C = C(1 + 0.11 + 0.12) = C(1.23)
\]

Thus, the **lowest price** is $ 1.23 \times C $.

Now, the problem asks for the lowest price based on covering only costs and overheads (not profit), which means we exclude the 12% profit from the calculation. In that case, the price would cover only cost and overhead, so:

\[
\text{Lowest Price without Profit} = C + 0.11C = C(1 + 0.11) = 1.11C
\]

So, the lowest price Get-Aways Company can charge to cover **costs and overheads** would be:
\[
1.11 \times C
\]

Since the current price they are charging is $3229, this includes both overhead and profit. To find the base cost $C$, we know the price equation is:
\[
3229 = 1.23C
\]

Now, solve for $C$:
\[
C = \frac{3229}{1.23} = 2626.02
\]

So, the cost $C$ is approximately $2626.02.

Finally, the lowest price that covers costs and overhead (without profit) is:
\[
1.11 \times 2626.02 = 2915.88
\]

Thus, the **lowest price** Get-Aways Company can offer, covering just the costs and overheads, is **$2915.88** per person.

Would you like further clarification or additional details?

Here are 5 related questions for further exploration:
1. How does an increase in overhead percentage affect the lowest possible price?
2. If the profit margin were reduced, what would the new price be?
3. What is the break-even point if the company offers a 5% discount?
4. How would a change in base costs affect both the cost-inclusive price and profit margin?
5. How can the company adjust its target profit to remain competitive?

**Tip**: Always separate fixed and variable costs when calculating pricing strategies to ensure a thorough understanding of cost drivers.

Find out how to calculate the lowest possible price for a sightseeing tour offered by Get-Aways Company while covering all costs and overhead expenses. This example uses key algebraic formulas for cost, overhead, and profit, ideal for high school students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation