To determine the price that maximizes revenue, we need to find the point at which the total revenue is highest. Revenue is calculated by multiplying the number of units sold by the price per unit.
Let's solve each scenario separately:
(A) For every $0.10 reduction in price, 40 more sandwiches are sold.
Let's denote the price reduction as "x" (in dollars) and the additional sandwiches sold as "y." According to the given information, we have the following relationship:
x = $0.10
y = 40
The original price is $8, so the new price would be $8 - x. The new number of sandwiches sold would be 640 + y.
The revenue is calculated as the product of the price and the number of sandwiches sold:
Revenue = (640 + y) * ($8 - x)
Substituting the given values:
Revenue = (640 + 40) * ($8 - $0.10)
= 680 * $7.90
= $5,372
Therefore, the deli should charge $7.90 for a sandwich to maximize revenue in this scenario.
(B) For every $0.20 reduction in the original $8 price, 15 more sandwiches are sold.
Using similar logic as in scenario (A), we have:
x = $0.20
y = 15
The new price would be $8 - x, and the new number of sandwiches sold would be 640 + y.
The revenue equation becomes:
Revenue = (640 + y) * ($8 - x)
Substituting the given values:
Revenue = (640 + 15) * ($8 - $0.20)
= 655 * $7.80
= $5,094
Therefore, the deli should charge $7.80 for a sandwich to maximize revenue in this scenario.
In summary, to maximize revenue:
(A) The deli should charge $7.90 per sandwich.
(B) The deli should charge $7.80 per sandwich.
credit goes to Neissus he did it all he has to be a teacher a cool one