The manager of a large apartment complex knows from experience that 110 units will be occupied if the rent is 342 dollars per month. A market survey suggests that, on the average, one additional unit will remain vacant for each 9 dollar increase in rent. Similarly, one additional unit will be occupied for each 9 dollar decrease in rent. What rent should the manager charge to maximize revenue? I know the rate of change for people relative to rent, but how do I express it mathematically? How do I solve the equations with symbols.I would multiply by the number of increments.
If I was programming, this would be my pseudocode: Prompt rent, people Revenue_0 = rent * people; dp/dr = -1/9; for n = 0, n = (rent+9), n++ dR/dr = (rent*(dp/dr*n))+Revenue_0= 0 revmax = Revenue @ DR/dr = 0 display ("Revmax =",revmax) I am trying to find the maximum value for revenue, but don't know how to include the number of times the rent is increased by $9 into the formula. Is my reasoning correct, or am I mistaken?