At a flea market held each weekend, an artist sells handmade earrings. The table below shows the average number of pairs of earrings sold for several prices. Given the pattern in the table, how much should the artist charge to maximize revenue?
Table:
price: $15 $14 $13 $12
pairs: 50 60 70 80
To determine how much the artist should charge to maximize revenue, we need to analyze the relationship between the price of the earrings and the number of pairs sold. Revenue is calculated by multiplying the price per pair by the number of pairs sold.
Looking at the pattern in the table, we can observe that as the price decreases, the number of pairs sold increases. This suggests an inverse relationship between price and demand.
To find the price that maximizes revenue, we need to identify the point at which the change in revenue starts to decline. This can be done by computing the revenue for each price point.
Let's calculate the revenue for each price point:
- Price $15 x Pairs 50 = Revenue $750
- Price $14 x Pairs 60 = Revenue $840
- Price $13 x Pairs 70 = Revenue $910
- Price $12 x Pairs 80 = Revenue $960
From the calculations, we can see that the revenue increases as the price decreases. However, the rate of increase starts to slow down as we move from $14 to $13. There is a decrease in the rate of return for decreasing prices.
Therefore, to maximize revenue, the artist should charge a price of $13, as it generates the highest revenue in the given pattern.