What price will maximize revenue and what is the maximum rev

What price will maximize revenue and what is the maximum revenue?

last month perfect fabric sold 250 m of braodcloth at $8/m the manager has a surplus that she wants to sell. She estimates that with each $.50 reduction in the price, she will sell an additional 50m.

Solution

The manager has sold 250 m at $8/m . Now with every 50 cents reduction in the price an additional 50 m are sold.

At $8/m 250 are sold, the revenue is 2000

So if at $7.5/m, 300 meters are sold, the revenue is 2250

at $7/m 350 m are sold and revenue is 2450

At $6.5/m 400 m are sold and revenue is 2600

At $6/m 450 m are sold and revenue is 2700

At $5.5/m 500 m are sold and revenue is 2750

At $5/m 550 m are sold and revenue is 2750

Therefore the maximum revenue is at $ 5.5/ m after which it starts decreasing.

The maximum revenue is $ 2750.