The following table gives the cost and revenue, in dollars, for different production levels, q. Answer the questions below.
q 0 100 200 300 400 500 600
R(q) 0 450 900 1350 1800 2250 2700
C(q) 670 865 990 1095 1255 1820 2590
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:
To answer these questions, we need to analyze the given data in the table.
1. The fixed costs are the costs that do not change with the level of production (q). Looking at the table, we can see that the cost (C) is given for different levels of production. However, since fixed costs remain constant, we can find the fixed costs by looking at the cost (C) for the smallest level of production (q = 0). Therefore, the fixed costs are $670.
2. The price charged per unit can be calculated by dividing the total revenue (R) by the quantity (q). Looking at the table, we find that the revenue (R) is given for different levels of production. Again, we can find the price per unit by dividing the revenue (R) by the quantity (q) for any given production level. Let's choose q = 100 for simplicity. The revenue (R) at q = 100 is $450. Dividing $450 by 100, we find that the price charged per unit is $4.50.
3. To determine the level of production at which profit is maximized, we need to calculate the profit for each level of production by subtracting the cost (C) from the revenue (R). We can then compare these profits to find the maximum value. Let's calculate the profit for each level of production:
q = 0: Profit = R(0) - C(0) = $0 - $670 = -$670
q = 100: Profit = R(100) - C(100) = $450 - $865 = -$415
q = 200: Profit = R(200) - C(200) = $900 - $990 = -$90
q = 300: Profit = R(300) - C(300) = $1350 - $1095 = $255
q = 400: Profit = R(400) - C(400) = $1800 - $1255 = $545
q = 500: Profit = R(500) - C(500) = $2250 - $1820 = $430
q = 600: Profit = R(600) - C(600) = $2700 - $2590 = $110
From the table, we can see that the profit is maximized at approximately q = 400 when the profit value is the highest ($545). Therefore, the answer is approximately 400 (rounded to the nearest 100).