Colli Real Estate

Help with calculating functions?

Ok, here's the question: Part 1: A real estate company manages 150 apartments in Irvine, California. All apartments can be rented at a price of $ 1200 per month, but for every $ 100 increase in monthly rent will be 5 new vacancies. a) An income Express Total monthly apartment rentals according to the p monthly rental fee for each unit. b) What price should the company charge to maximize revenue total? How much income? Part 2: Suppose that costs $ 500 per month for the company above to maintain the property and promote individual unrented unit. A) Enter the total monthly income of R obtained by apartments according to the P monthly rental fee for each unit. b) What p monthly prices rental company should charge to maximize total revenue? How much income? Thank you!

Part 1 a) Let x = the number of apartments let R = x * px = 150 – 5 * (P-1200) / 100 x = 150 – (p-200) / 20 x = 60 x = 150-p/20 210 -p/20 R = ^ p-210p 2 / 20 b) Differentiate the equation above DR / DP = 210-p/10 (= 0 to max or min) 210-p/10 p = 0 = 2100 for income of $ 220,500 Max R max = Part 2) x = 210-p/20 R = 210p-p ^ 2 / 20 -500 * (150-x) R = 210p-p ^ 2 / 20 * -500 (150-210 + p/20) R = 210p-p ^ 2 / 20 30000-25 R p = 185p-p ^ 2 / 20 30000 b) distinguishing dr / DP = 185-p/10 185-p/10 = 0 p = 1850 for the highest income, after paying the $ 201,125 advertising Rmax Note that at this price 117.5 apartments are rented. To have an integer apartments for rent, a rent of $ 1840 or $ 1860 is required. Anyone would after the advertising revenue of $ 201,120 per month.

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