Need help with this maximization problem.

[ccooper5867]

There are 100 places at a restaurant, each place yields an average income of $45 dollars per day. Each additional place will decrease 30 cents per place. How many places should be added in order to maximize the daily income of the restaurant?

 

[lookagain]

There are 100 places at a restaurant, each place yields an average income of $45 dollars per day.
Each additional place will decrease 30 cents per place. How many places should be added in order to maximize the daily
income of the restaurant?

If I show you a possible set-up, you should have enough calculus and algebra ability to solve the problem,

or at least get most of it done.

Define your variable: Let x = the number of places in the restaurant to be added

To simplify things in the expression, I will not use units for money.

Daily income = (# of places at the restaurant) multiplied by the (average income each place yields per day)


Daily Income = (100 + x)(45 - .30x) \(\displaystyle \ \ \) *


Now, you must solve for x, by using calculus, that will maximize the daily income.


You should be able to continue from there. *



Please show your work here.

 

[stapel]

There are 100 places at a restaurant, each place yields an average income of $45 dollars per day. Each additional place will decrease 30 cents per place. How many places should be added in order to maximize the daily income of the restaurant?

You can use what you learned back in algebra to do the set-up, like in the example at the bottom of the page here. If you're not confident of the set-up suggested by the previous reply, try plugging numbers into the exercise, to find the pattern, like they show at the link. Keep plugging in until you see the pattern for yourself!