Step-by-Step Solution:
1. Obtain the past sales data for yellow golf balls:
- Year 1: 204,132 golf balls
- Year 2: 225,624 golf balls
- Year 3: 237,108 golf balls
2. Calculate the year-over-year increase rates for yellow golf balls:
- Increase from Year 1 to Year 2:
[tex]\[
\text{Increase Rate}_1 = \frac{\text{Year 2 Sales} - \text{Year 1 Sales}}{\text{Year 1 Sales}} = \frac{225,624 - 204,132}{204,132} = \frac{21,492}{204,132} \approx 0.1053 \text{ or } 10.53\%
\][/tex]
- Increase from Year 2 to Year 3:
[tex]\[
\text{Increase Rate}_2 = \frac{\text{Year 3 Sales} - \text{Year 2 Sales}}{\text{Year 2 Sales}} = \frac{237,108 - 225,624}{225,624} = \frac{11,484}{225,624} \approx 0.0509 \text{ or } 5.09\%
\][/tex]
3. Calculate the average increase rate over the two periods:
[tex]\[
\text{Average Increase Rate} = \frac{\text{Increase Rate}_1 + \text{Increase Rate}_2}{2} = \frac{0.1053 + 0.0509}{2} \approx 0.0781 \text{ or } 7.81\%
\][/tex]
4. Estimate the sales of yellow golf balls for Year 4 using this average increase rate:
[tex]\[
\text{Estimated Year 4 Sales (Yellow)} = \text{Year 3 Sales} \times (1 + \text{Average Increase Rate}) = 237,108 \times (1 + 0.0781) \approx 255,624
\][/tex]
5. Given the ratio of yellow to white golf ball sales in Year 4 is 1:5, calculate the sales of white golf balls:
[tex]\[
\text{Estimated Year 4 Sales (White)} = \text{Estimated Year 4 Sales (Yellow)} \times 5 = 255,624 \times 5 = 1,278,120
\][/tex]
6. Calculate the total number of golf balls sold (yellow + white) in Year 4:
[tex]\[
\text{Total Sales (Both Colors)} = 255,624 + 1,278,120 = 1,533,744
\][/tex]
7. Calculate the total revenue from selling these golf balls. Given the average price per box (12 golf balls) is [tex]$23.94:
\[
\text{Total Revenue} = \left(255,624 + 1,278,120\right) \times 23.94 = 1,533,744 \times 23.94 \approx 36,717,859.68
\]
Final Answer:
The company's estimated total sales of golf balls in Year 4 is approximately \$[/tex]36,717,859.68.
