Explanation:
To find the price that maximizes Caleb's revenue, we need to determine the optimal price point at which he can maximize his total revenue, given the constraint that each time he raises the price by $20, he loses one customer.
Let's first calculate Caleb's current total revenue:
Total revenue = Price x Quantity
Total revenue = $100 x 8
Total revenue = $800
Now, let's assume that Caleb increases his price by $20. This means that his new price will be $120, and he will lose one customer. Therefore, his new quantity will be 7.
New revenue = New price x New quantity
New revenue = $120 x 7
New revenue = $840
We can repeat this process for each subsequent price increase and calculate the new revenue at each price point:
Price = $120, Quantity = 7, Revenue = $840
Price = $140, Quantity = 6, Revenue = $840
Price = $160, Quantity = 5, Revenue = $800
Price = $180, Quantity = 4, Revenue = $720
Price = $200, Quantity = 3, Revenue = $600
Price = $220, Quantity = 2, Revenue = $440
Price = $240, Quantity = 1, Revenue = $240
As we can see from the calculations above, the price that maximizes Caleb's revenue is $120. At this price point, Caleb can generate the highest revenue of $840. If Caleb increases his price further, his revenue will start to decline due to the decrease in quantity, as customers drop off.