Yahoo Answers: Answers and Comments for Need Help Quickly PLEASE in Calculus Optimization in Economics? [Mathematics]
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From Kal
enSG
Tue, 25 Jun 2019 20:12:51 +0000
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Yahoo Answers: Answers and Comments for Need Help Quickly PLEASE in Calculus Optimization in Economics? [Mathematics]
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From Captain Matticus, LandPiratesInc: Income  Cost = Profit
(460 + 25 * x) * (150 ...
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https://sg.answers.yahoo.com/question/index?qid=20190625201251AAcdx11
Tue, 25 Jun 2019 20:29:09 +0000
Income  Cost = Profit
(460 + 25 * x) * (150  4 * x)  72.50 * 150 = P
P = 460 * 150 + 25 * 150 * x  460 * 4 * x  100 * x^2  7250
P = 46 * 15 * 100  7250 + 3750x  1840x  100x^2
P = 69000  7250 + 1910x  100x^2
dP/dx = 0 + 1910  200x
dP/dx = 0
0 = 1910  200x
0 = 191  20x
20x = 191
x = 191/20
x = 95.5/10
x = 9.55
x = 9 or x = 10. Maybe even x = 9.5. By the way, I'm assuming that the utilities and repairs go for each unit, whether or not they're occupied. We can change things later if we wish
x = 9.5
P = 69000  7250 + 1910x  100x^2
P = 61750 + 1910 * 9.5  100 * 9.5^2
P = 61750 + 191 * 95  100 * (19/2)^2
P = 61750 + 191 * (100  5)  100 * (361/4)
P = 61750 + 19100  955  36100/4
P = 80850  955  9025
P = 71825  955
P = 72000  175  955
P = 71045  175
P = 71000  135
P = 70865
460 + 25 * 9.5 = 460 + 250  12.5 = 710  12.5 = 697.5
Assuming that utilities and repairs only apply to apartments that are rented
P = (460 + 25 * x) * (150  4x)  72.5 * (150  4x)
P = (460  72.5 + 25 * x) * (150  4x)
P = (387.5 + 25x) * 2 * (75  2x)
P = (775 + 50x) * (75  2x)
P = 25 * (31 + 2x) * (75  2x)
dP/dx = 25 * (31 + 2x) * (2) + 25 * (75  2x) * 2
dP/dx = 0
0 = 25 * 2 * (75  2x  31  2x)
0 = 75  31  4x
0 = 44  4x
4x = 44
x = 11
460 + 25 * 11
460 + 275
735
Rent should be $735 per month. Considering that the numbers work nicer with this assumption, I'm going to go ahead and say that this is what they wanted.
P = 25 * (31 + 2x) * (75  2x)
P = 25 * (31 + 22) * (75  22)
P = 25 * 53 * 53
P = 25 * (52 + 1)^2
P = 25 * (52^2 + 2 * 52 + 1)
P = 25 * 52 * 52 + 25 * 2 * 52 + 25 * 1
P = 25 * 4 * 13 * 52 + 50 * 52 + 25
P = 100 * 13 * 13 * 4 + 100 * 26 + 25
P = 100 * 169 * 4 + 2600 + 25
P = 100 * 676 + 2625
P = 67600 + 2625
P = 70225

From Mike G: Points given are (460,150) and (485,146)
x = ...
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https://sg.answers.yahoo.com/question/index?qid=20190625201251AAcdx11
Wed, 26 Jun 2019 00:27:17 +0000
Points given are (460,150) and (485,146)
x = Rent, y = Units occupied
Slope = 4/25 = 0.16
Linear equation
y150 = 0.16(x460)
y = 0.16x + 223.6
R = Revenue = xy = 0.16x^2+223.6x
C = Costs = 72.5y = 11.6x+16211
P = Profit = RC
P = 0.16x^2+223.6x+11.6x16211
P = 0.16x^2+235.2x16211
dP/dx = 0.32x+235.2 = 0 for maximum
x = 235.2/0.32 = 735
Answer $735 per month