Question

I am having a hard time figuring this out. I know I need to find the vertex from the vertex form equation but I am having a hard time figuring out the equation.

A caterer will charge a certain club $20 per member to cater a dinner if 150 members attend. However, the cost per member will be reduced by 80 cents for each member attending in excess of 150. What is the maximum revenue that the caterer can make? If you were the caterer, what upper limit would you set for the number of members that can attend the dinner?

So far I have this equation:
price per member = 20 - 0.80 (y - 150)

Answer 1

Ok. So, the revenue is the price times the attendance:

(20-.80(y-150))(y) for y >= 150

You sure there's no typo? I get a maximum revenue for y < 150.

Maybe the first 150 still get charged $20, but the extras get charged less. In that case, for y>150, the revenue is

20*150 + (20-.8(y-150))(y-150)

Then the maximum is at y=162 and it drops back to 3000 at y=175.