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Consider a town in which only two residents, Shen and Valerie, own wells that produce water safe for drinking. Shen and Valerie can pump and sell as much water as they want at no cost. For them, total revenue equals profit. The following table shows the town's demand schedule for water.

\begin{tabular}{ccc}
Price & \begin{tabular}{c} Quantity Demanded \\ (Gallons of water) \end{tabular} & \begin{tabular}{c} Total Revenue \\ (Dollars) \end{tabular} \\
\hline
\[tex]$5.40 & 0 & \$[/tex]0 \\
\[tex]$4.95 & 40 & \$[/tex]198.00 \\
\[tex]$4.50 & 80 & \$[/tex]360.00 \\
\[tex]$4.05 & 120 & \$[/tex]486.00 \\
\[tex]$3.60 & 160 & \$[/tex]576.00 \\
\[tex]$3.15 & 200 & \$[/tex]630.00 \\
\[tex]$2.70 & 240 & \$[/tex]648.00 \\
\[tex]$2.25 & 280 & \$[/tex]530.00 \\
\[tex]$1.80 & 320 & \$[/tex]486.00 \\
\[tex]$1.35 & 360 & \$[/tex]360.00 \\
\[tex]$0.90 & 400 & \$[/tex]198.00 \\
\[tex]$0.45 & 440 & \$[/tex]0 \\
\hline
\end{tabular}

Sagot :

GinnyAnsweridn
To determine the missing values in the table, we need to understand the relationship between price, quantity demanded, and total revenue. Here's a step-by-step guide to fill in the table:

1. Columns Provided:
- Price (P): Given.
- Quantity Demanded (Q): Given.
- Total Revenue (TR): Some values are missing and need to be determined.

2. Total Revenue Calculation:
- Total Revenue (TR) = Price (P) × Quantity Demanded (Q)

Using the provided values, let's verify the calculations and fill in any missing values:

| Price (P) | Quantity Demanded (Q, Gallons) | Total Revenue (TR, Dollars) |
|-------|--------------------------|-----------------------------|
| 5.40 | 0 | 0 |
| 4.95 | 40 | 4.95 × 40 = 198.00 |
| 4.50 | 80 | 4.50 × 80 = 360.00 |
| 4.05 | 120 | 4.05 × 120 = 486.00 |
| 3.60 | 160 | 3.60 × 160 = 576.00 |
| 3.15 | 200 | 3.15 × 200 = 630.00 |
| 2.70 | 240 | 2.70 × 240 = 648.00 |
| 2.25 | 280 | 2.25 × 280 ≠ 530.00 (Check value)|
| 1.80 | 320 | 1.80 × 320 = 576.00 |
| 1.35 | 360 | 1.35 × 360 = 486.00 |
| 0.90 | 400 | 0.90 × 400 = 360.00 |
| 0.45 | 440 | 0.45 × 440 = 198.00 |
| 0.00 | 480 | 0.00 × 480 = 0 |

Notice there was an error in the table provided in the question for the total revenue at price 2.25. The correct value should be calculated using the formula:

[tex]\[ \text{Total Revenue} = 2.25 \times 280 = 630.00 \][/tex]

So the corrected table is:

| Price (P) | Quantity Demanded (Q, Gallons) | Total Revenue (TR, Dollars) |
|-------|--------------------------|---------------------------|
| 5.40 | 0 | 0 |
| 4.95 | 40 | 198.00 |
| 4.50 | 80 | 360.00 |
| 4.05 | 120 | 486.00 |
| 3.60 | 160 | 576.00 |
| 3.15 | 200 | 630.00 |
| 2.70 | 240 | 648.00 |
| 2.25 | 280 | 630.00 |
| 1.80 | 320 | 576.00 |
| 1.35 | 360 | 486.00 |
| 0.90 | 400 | 360.00 |
| 0.45 | 440 | 198.00 |
| 0.00 | 480 | 0 |

By understanding the total revenue formula and recalculating the required values, we have determined the correct total revenue amounts.
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