Solve Min-Max Problem: Find Optimal Price of Single Call

[Yankel]

Hello, I need some help with this simple question, don't know why I got it wrong...

The price of a single phone call is 0.5\$ and the average number of calls made in a month is 200.

For each 5 cent of price increment, the average number of calls made by the customers decreases by 10.

Find what should be the cost of a single call so that the income will be maximal.

I know I need to build up a function and then find derivative and all that, I just can't build the right function...
The final answer is by the way 0.75\$.

Thank you

 

[earboth]

Hello, I need some help with this simple question, don't know why I got it wrong...

The price of a single phone call is 0.5 USD and the average number of calls made in a month is 200.

For each 5 cent of price increment, the average number of calls made by the customers decreases by 10.

Find what should be the cost of a single call so that the income will be maximal.

I know I need to build up a function and then find derivative and all that, I just can't build the right function...
The final answer is by the way 0.75$.

Thank you

1. Please don't use the dollar sign.

2. Let x be the number of 5-cts-increment. Then the income is determined by:

$ \displaystyle{f(x)=(0.5 + 0.05 \cdot x)(200-10x)} $

3. Go ahead!