Until recently hamburgers at the city sports arena cost $4 each. The food concessionaire sold an average of 10,000 hamburgers on a game night. When the price was raised to $4.40, hamburger sales dropped off to an average of 8,000 per night. Assuming a linear demand curve, find the price of a hamburger that will maximize the nightly hamburger revenue. If the concessionaire has a fixed cost of $1000 per night and the variable cost is $0.60 per hamburger, find the price of a hamburger that will maximize the nightly hamburger profit.

a) Price that maximize revenue P=$3

b) Price that maximize revenue (with costs) P=$3.3

Explanation:

We assume a linear demand curve as:

With the data given, we can calculate the parameters m and Q0:

Then, the demand equation becomes

The revenue can be defined as:

To maximize the revenue, we derive and equal to zero:

We now modify the revenue equation to include the fixed and variable cost, and derive again:

muslims control the north africa during the period of 1500 up

to 1800. they made a barrier to prevent further european exploration from

entering the africa from the north. however, the dutch ware still able to move

toward the interior with having south africa as one of the routes leading to

the east for trading with asia.