If there are x price decreases, then
price = 6.00 - .25x or 6-x/4
demand = 330 + 15x
Since revenue = price * quantity,
r(x) = (6-x/4)(330+15x)
= -15/4 x^2 + 15/2 x + 1980
Now use what you know about parabolas to find the vertex. Since this parabola opens downward, the vertex is the maximum revenue.
But it is the max revenue for a given number of price increases. To answer the question, you need to figure out what the actual price is.
A restaurant sells about 330 sandwiches each day at a
price of $6 each. For each $.25 decrease in price, 15 more sandwiches are sold
per day. How much should the restaurant charge to maximize daily revenue?
Explain each step of your solution. What is the maximum daily revenue?
1 answer