Let's analyze the given situation step by step.
Mike expects the revenue to increase by [tex]$100 with each mobile phone sold up to a maximum of $[/tex]70,000. After reaching this maximum revenue, the revenue will drop by [tex]$100 with each additional unit sold.
Firstly, we need to find the equations that model this situation.
1. Evaluating the Equations:
- Equation 1: \( r = -1001x - 7001 + 70,000 \)
- Equation 2: \( r = -1001x - 70000 + 70,000 \)
- Equation 3: \( r = -1x - 100 + 70,000 \)
By comparing these equations to the given conditions, we can see that:
- The drop in revenue per unit sold after the target is $[/tex]100, thus relevant equations would have the term "-100" or similar. Check which of the equations captures the correct drop in revenue and add the maximum revenue amount to verify.
Based on the conditions and the output:
- Equation 3: [tex]\( r = -1x - 100 + 70,000 \)[/tex]
This equation is the most accurate model as it correctly deducts [tex]$100 per unit sold after reaching the target with an offset at $[/tex]70,000.
Hence, the correct equation is:
The equation that models the revenue is [tex]\( r = -1 x - 100 + 70,000 \)[/tex].
2. Checking the Revenue for Given Units:
- For 500 units:
The revenue for 500 units is:
Given target: 20000
- For 900 units:
The revenue for 900 units is:
Given target: -20000
Thus, it's confirmed:
Revenue will be [tex]$20,000 for 500 units and -20,000 for 900 units.
So, let's identify the correct statements:
- The equation that models the revenue is \( r = -1 x - 100 + 70,000 \).
- Revenue will be $[/tex]20,000 for 500 units and [tex]$-20,000$[/tex] for 900 units.
Hence, the correct selections among the statements provided would be:
1. The equation that models the revenue is [tex]\( r=-1 x -100 + 70,000\)[/tex].
The numerical values prove that the only correct statement according to this solution are those that mentions true equation. Analyzing all provided statements with correct result can be computed to reach accurately.
So, the answer is:
- The equation that models the revenue is [tex]\( r=-1x -100+70,000\)[/tex].
