I'm stuck on a story problem, so please if anybody could help me

on3winyoureyes

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[h=1][/h]The Edgewater Hotel has 210 guest rooms. When they charge a discounted rate of $250 per night, the occupancy rate is 80%. Experience has shown that each $10 increase in rate results in a 5 fewer occupied rooms.

a) Define the function that models the total revenue to the hotel as a function of x, the number of $10 price increases.

b) If prices may increase by any whole dollar amount (not just by tens), find the nightly rate that will maximize the nightly revenue. Round to the nearest dollar.

I honestly don't know how to get started. I thought it was a linear programming problem but when I tried putting the ideas into equations, I just got even more confused.
 
The Edgewater Hotel has 210 guest rooms. When they charge a discounted rate of $250 per night, the occupancy rate is 80%. Experience has shown that each $10 increase in rate results in a 5 fewer occupied rooms.
a) Define the function that models the total revenue to the hotel as a function of x, the number of $10 price increases.
We must assume that the $250 is per room.
With no rise in rate the revenue is \(\displaystyle 0.8\cdot 210\cdot 250=42000\).

Suppose we increase the rate three times to $280.
The revenue is \(\displaystyle (0.8\cdot 210-5\cdot 3)\cdot(250+10\cdot3)=42840\).

With x number of rate increases, the revenue is \(\displaystyle (0.8*210-5x)*(250+10\cdot x)\).
 
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