Page of 10 - ZOOM + 4. All units in a 50-unit apartment building are rented out when the rent is set at r = $1500 per month. A survey reveals that for each $50 increase in rent, demand for apartments will decrease, such that one additional apartment becomes vacant. Suppose that each occupied unit costs $100 per month in maintenance. a. Define variables to maximize monthly profit. Write occupied units as a function of rent. b. Determine profit function as a function of single variable. What is the domain on which you should consider this function? [1)Page of 10 - ZOOM + c. Which rent r maximizes monthly profit? [1] d. What is the Maximum profit? [1]Page 5 > of 10 - ZOOM + 5. Let f(x) = 2x4 - 3x2 + 1 then (a) Find the critical numbers [1] (b) Find the points of inflection [1]Page of 10 - ZOOM + (c) Find the intervals on which f is increasing or decreasing [1] (d) Find the intervals on which f is concave up or down [1]