Questions: The following table gives the cost and revenue, in dollars, for different production levels, q. q 0 100 200 300 400 500 600 ------------------------------------ R(q) 0 480 960 1440 1920 2400 2880 C(q) 675 865 1010 1100 1275 1815 2635 1. The fixed costs are dollars 2. The price charged per unit is dollars 3. At approximately what level of production q, is the profit maximized? Round your answer to the nearest 100 . Answer: units

The following table gives the cost and revenue, in dollars, for different production levels, q.

q 0 100 200 300 400 500 600
------------------------------------
R(q) 0 480 960 1440 1920 2400 2880
C(q) 675 865 1010 1100 1275 1815 2635

1. The fixed costs are dollars
2. The price charged per unit is dollars
3. At approximately what level of production q, is the profit maximized? Round your answer to the nearest 100 .
Answer: units

Transcript text: The following table gives the cost and revenue, in dollars, for different production levels, $q$. Answer the questions below. \begin{tabular}{|c|c|c|c|c|c|c|c|} \hline q & 0 & 100 & 200 & 300 & 400 & 500 & 600 \\ \hline $\mathrm{R}(\mathrm{q})$ & 0 & 480 & 960 & 1440 & 1920 & 2400 & 2880 \\ \hline $\mathrm{C}(\mathrm{q})$ & 675 & 865 & 1010 & 1100 & 1275 & 1815 & 2635 \\ \hline \end{tabular} 1. The fixed costs are dollars 2. The price charged per unit is dollars 3. At approximately what level of production $q$, is the profit maximized? Round your answer to the nearest 100 . Answer: $\square$ units

Solution

Solution Steps

To solve the given questions, we need to analyze the provided cost and revenue data for different production levels.

Fixed Costs: Fixed costs are the costs that do not change with the level of production. From the table, the cost at production level $ q = 0 $ is the fixed cost.
Price Charged Per Unit: The price per unit can be determined by the change in revenue divided by the change in production level.
Profit Maximization: Profit is maximized where the difference between revenue and cost is the greatest. We need to calculate the profit for each production level and find the maximum.

Step 1: Fixed Costs

The fixed costs are determined from the cost at production level $ q = 0 $. From the table, we have: \[ \text{Fixed Costs} = C(0) = 675 \]

Step 2: Price Charged Per Unit

The price charged per unit can be calculated using the change in revenue divided by the change in production level. For the first production level: \[ \text{Price per Unit} = \frac{R(100) - R(0)}{100 - 0} = \frac{480 - 0}{100} = 4.8 \]

Step 3: Profit Maximization

Profit is calculated as the difference between revenue and cost for each production level: \[ \text{Profit}(q) = R(q) - C(q) \] The profits for each production level are: