Owners of a toy car company have determined that if they charge customers dollars per car, where 1p80, the number of cars in inventory, .. can be modeled by the linear function .( )=10a /12. If they charge $1 per car or less, they will sell all their cars. If they charge $80 per car or more, they will not sell any cars. Assuming the owners plan to charge customers between $1 and $80 per car, how much should they charge to maximize their revenue?

The revenue will be given by R=np. They will not accept negative revenue figures because then they will lose money.

Method 1: graph revenue function and determine the maximum value in the closed interval [1,80]. Show a picture of the graph. Method 2: Use calculus techniques to find the maximum function in the closed interval [1,80]. Be sure to identify all critical points and justify the answer.

Now suppose the owners decide that no one will pay more than $4 for a toy car, and therefore, they will charge no more than $4. Assuming the owners plan to charge customers between $1 and $4 per car, how much should they now charge to maximize their revenue?

Method 1: determine the maximum value in the closed interval [1,4]. Method 2: Use calculus techniques to find the maximum function in the closed interval [1,4].