Suppose that a company wishes to predict sales volume based on the amount of advertising expenditures. The sales manager thinks that sales volume and advertising expenditures are modeled according to the following linear equation. Both sales volume and advertising expenditures are in thousands of dollars.
 
Estimated Sales Volume=48.81+0.49(Advertising Expenditures)

If the company has a target sales volume of $125,000
, how much should the sales manager allocate for advertising in the budget? Round your answer to the nearest dollar.

The given equation for the estimated sales volume (in thousands of dollars) based on advertising expenditures is:

\[
\text{Sales Volume} = 48.81 + 0.49 \times \text{Advertising Expenditures}
\]

The company has a target sales volume of $125,000, which is equivalent to 125 in thousands of dollars. We need to find the advertising expenditure required to achieve this sales target. Let's plug in the sales volume of 125 and solve for the advertising expenditure.

\[
125 = 48.81 + 0.49 \times \text{Advertising Expenditures}
\]

First, subtract 48.81 from both sides:

\[
125 - 48.81 = 0.49 \times \text{Advertising Expenditures}
\]

\[
76.19 = 0.49 \times \text{Advertising Expenditures}
\]

Now, divide both sides by 0.49:

\[
\text{Advertising Expenditures} = \frac{76.19}{0.49} \approx 155.49
\]

Rounding to the nearest dollar:

\[
\text{Advertising Expenditures} \approx 155
\]

Therefore, the sales manager should allocate **$155,000** for advertising.

Would you like a detailed explanation of the steps, or do you have any questions?

Here are five related questions:
1. How would the advertising expenditure change if the target sales volume is $150,000?
2. What is the minimum sales volume when there is no advertising expenditure?
3. How does the coefficient 0.49 affect the relationship between sales volume and advertising expenditures?
4. What would happen to sales volume if the advertising expenditure were doubled?
5. How would the model change if we introduced another factor, such as market conditions?

**Tip:** When working with linear equations in real-world problems, always keep track of the units (like thousands of dollars here) to ensure consistency in calculations.

Suppose that a company wishes to predict sales volume based on the amount of advertising expenditures. The sales manager thinks that sales volume and advertising expenditures are modeled according to the following linear equation. Both sales volume and advertising expenditures are in thousands of dollars. Estimated Sales Volume = 48.81 + 0.49 (Advertising Expenditures). If the company has a target sales volume of $125,000, how much should the sales manager allocate for advertising in the budget? Round your answer to the nearest dollar.

Learn how to predict sales volume based on advertising expenditures using the linear equation Sales Volume = 48.81 + 0.49 * Advertising Expenditures. Find out how much a company needs to allocate for advertising to meet a target sales volume of $125,000. This problem covers key algebraic concepts and is suitable for students in Grades 9-12.

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