6. A landlord manages 100 apartments in a complex downtown and charges his tenants monthly. When the rent is $800 a month, all of the apartments are rented. For every $15 increase in rent, one apartment becomes empty. On average, each apartment needs $60 invested in maintenance and repairs each month. The landlord wants to know how much he should charge per month in order to have the greatest profit. Could he make a greater profit without all of the apartments rented? Explain. [C/10]Optimization - Algorithm 1. Read and understand the problems text 2. Draw a diagram (if necessary). 3. Assign variables to the quantities involved and state restrictions according to the situation. 4. Write relations between these variables. 5. Identify the variable that is minimized or maximized. This is the dependent variable 6. Use the other relations (called constraints) to express the dependent variable (the one which is minimized or maximized) as a function of one single variable (the independent variable). 7. Find extrema (maximum or minimum) for the dependant variable (using global extrema algorithm, first or second derivative test). 8. Check if extrema satisfy the conditions of the application. 9. Find the value of other variables at extrema (if necessary). 10. Write the conclusion statement