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

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To solve the min-max problem for determining the optimal price of a single phone call, the income function can be expressed as f(x) = (0.5 + 0.05x)(200 - 10x), where x represents the number of 5-cent increments. The average number of calls decreases by 10 for each increment of 5 cents in price. To find the maximum income, the derivative of the function should be calculated and set to zero. The optimal price for maximizing income is determined to be 0.75. This approach effectively combines price adjustments with customer call behavior to identify the best pricing strategy.
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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
 
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Yankel said:
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!
 
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