a surfboard shop sells 40 surfboards per month when it charges $500 per surfboard. Each time the shop decreases the price by $10, it sells 1 additional surfboard per month. how much should the shop charge per surfboard to maxamize the amount of money earned? what is the maximum amount the shop can earn per month? Explain.

Solution:

Find the mathematical model to represent this situation.

P = (40+x) (500-10x), where P equals Profit

Placing the model in standard form we get,

P = - 10x²+100x+20000

To find the maximum value, find the vertex of the quadratic model

x = - b/2a = - 100/2 (-10) = - 100/-20 = 5

so,

P = - 10 (5) ² + 100 (5) + 20000

P = 20,250

The maximum amount the shop can earn per month is $20,250.

The shop should charge [500-10 (5) ]=$450 per surfboard