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Question 1181229: Each month ZV Corp (Zebra Vehicles where all paint jobs are striped) makes 230 A vehicles which get 10mpg,500 B vehicles which get 20mpg,and 70 C vehicles which get 40mpg. Unfortunately, the government sets a standard where companies must “average”30mpg[this is called a CAFElaw]. Any company that falls short of the 30mpg standard must pay a penalty. The penalty is calculated as $55times number of vehicles sold each month times the deficit in their average mpg from the 30mpg standard.
Compute ZV Corp’s monthly penalty if the correct Harmonic Mean is used.
Answer by CPhill(1959)   (Show Source):
You can put this solution on YOUR website! Here's how to calculate ZV Corp's new monthly penalty:
1. **Calculate the total miles driven by each vehicle type:**
* A vehicles: 230 vehicles * 10 mpg = 2300 miles
* B vehicles: 500 vehicles * 20 mpg = 10000 miles
* C vehicles: 70 vehicles * 40 mpg = 2800 miles
* D vehicles: 2 vehicles * 75 mpg = 150 miles
2. **Calculate the total miles driven by all vehicles:**
Total miles = 2300 + 10000 + 2800 + 150 = 15250 miles
3. **Calculate the total number of vehicles:**
Total vehicles = 230 + 500 + 70 + 2 = 802 vehicles
4. **Calculate the company's average mpg:**
Average mpg = Total miles / Total vehicles
Average mpg = 15250 / 802
Average mpg ≈ 19.015 mpg
5. **Calculate the mpg deficit:**
Deficit = Standard mpg - Company average mpg
Deficit = 30 mpg - 19.015 mpg
Deficit ≈ 10.985 mpg
6. **Calculate the total penalty:**
Penalty = $55 * Total vehicles * Deficit
Penalty = $55 * 802 * 10.985
Penalty ≈ $485,355.70
Therefore, ZV Corp's new monthly penalty is approximately $\boxed{485,355.70}$.
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