An apartment building has 140 apartments, all renting at the same price. It is know that all the apartments can be rented if the rent is $250 per month, and that each increase in rent by $5 will result in one additional apartment becoming vacant. The rent (in dollars) producing the maximum total revenue is? And the maximum total revenue (in dollars) is?

Is it possible to solve this question on a TI-83?

To solve this question using a TI-83 calculator, you can use a graphing function called a quadratic regression. Here's how you can do it:

1. First, let's define the variables:
- x: the number of $5 increases in rent
- y: the number of rented apartments

2. Based on the information given, we can deduce that the number of rented apartments is given by the equation:
y = 140 - x

3. The total revenue can be calculated by multiplying the rent by the number of rented apartments. Therefore, the equation for the total revenue is:
R = (250 + 5x)(140 - x)

4. Enter the equation R = (250 + 5x)(140 - x) into your TI-83 calculator.

5. To find the rent producing the maximum total revenue, use the regression feature of your TI-83 calculator to find the maximum point of the graph. Here's how to do it on a TI-83:
- Press the STAT button.
- Select "Edit" and input the corresponding values of x and R.
- Go back to the STAT menu and select "Calc."
- Choose "QuadReg" or "Quadratic Regression."
- Input the variables so that your equation appears.
- Press ENTER to see the results.

The calculator will give you the value of x (the number of $5 increases in rent) that corresponds to the maximum total revenue. From there, you can calculate the actual rent that produces the maximum total revenue.

Remember to round the value to the nearest dollar, as rents are typically given in whole numbers of dollars and cents.