Thread: Demand Equation; Domain

The price, p and the quantity x sold of a certain product ovey the demand equation
x=10000 - 200p
A: Find a model that expresses the revenue R as a function of p

B: What is the domain of R?

C:What unit price should be used to maximize revenue?

D: If this price is changed, what is the maximum revenue?

E: How many units are sold at this price?

F: What price should be charged to collect at least $80000 in revenue?

Originally Posted by britta

The price, p and the quantity x sold of a certain product ovey the demand equation
x=10000 - 200p
A: Find a model that expresses the revenue R as a function of p

revenue = (price)(quantity sold)

B: What is the domain of R?

use the revenue equation and the fact that p and R > 0

C:What unit price should be used to maximize revenue?

the revenue function will be quadratic ... max revenue at the vertex

D: If this price is changed, what is the maximum revenue?

evaluate revenue at the price that maximizes it

E: How many units are sold at this price?

evaluate the demand function at the price

F: What price should be charged to collect at least $80000 in revenue?

set revenue = 80000 , you should get two possible solutions for p

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