A bakery has fixed monthly expenses of $\$ 1,200$ for rent and $\$ 300$ for insurance. Its variable expenses are $\$ 0.50$ per loaf of bread produced, plus $\$ 200$ for other variable costs. Write the equation that models the total monthly expenses, $E(q)$, based on the number of loaves of bread produced, $q$.

A$E(q)=0.50 q+1,200-500$
B$E(q)=0.50 q+1,700$
C$E(q)=0.50 q+1,500-200$
D$E(q)=0.50 q+1,500$

To model the total monthly expenses $E(q)$ for the bakery, we must categorize all costs into fixed expenses and variable expenses. Fixed expenses are costs that do not depend on the number of loaves produced, while variable expenses change based on the production volume $q$. The fixed monthly expenses are rent at $\$1,200$ and insurance at $\$300$. The variable expenses are $\$0.50$ per loaf produced, plus an additional $\$200$ for other variable costs.

Formulating the Equation for E(q)

First, we sum the fixed costs:
\[\text{Total Fixed Expenses} = 1,200 + 300 = 1,500\]
Next, we express the total variable costs, which depend on the number of loaves $q$:
\[\text{Total Variable Expenses} = 0.50q + 200\]
The total monthly expense $E(q)$ is the sum of these two categories:
\[E(q) = (1,500) + (0.50q + 200)\]
\[E(q) = 0.50q + 1,500 + 200\]
\[E(q) = 0.50q + 1,700\]

Identifying the Correct Option

Comparing our result $E(q) = 0.50q + 1,700$ with the given options:

A$E(q) = 0.50q + 1,200 - 500 = 0.50q + 700$

B$E(q) = 0.50q + 1,700$

C$E(q) = 0.50q + 1,500 - 200 = 0.50q + 1,300$

D$E(q) = 0.50q + 1,500$

The correct equation is found in option b.

Examples

Understanding how to model costs is crucial for any business owner, from a small local bakery to a large manufacturing company. By writing a cost function, a business owner can easily forecast their monthly spending based on different production targets. This allows for better financial planning, pricing strategy adjustments, and overall profitability analysis. For example, if a business knows their total cost function, they can determine the break-even point by setting the total revenue equal to the total expenses.