Question

The rent of an apartment is given by P (x) = 10x ^ 2 + 1760x-50000, what is the maximum possible profit?

Answer 1

lon? value - O The rent of the apartment is given by Pln) +176on 50000 plim) 20x + 1760 p" (3) 20 (1) In the of P(m) we maximum/mininum get p'in -> 201 +1760 = 0 1760 77 F-83 20 and P" (-88) = 2000 by (1) since p"(-88) 70 there P(n) has minimum value at the point na and no maximum is found for P(2) Therefore given question is wrong 88 1 .

Sign of Let us give an example related to your problem which has maximum value (Just changing het us consider P(n) as first term) Plu) -10%? +1760 X - 50000 Pino -200 t1760 P" (x ) At the maximum/ minimum value of Plo) get f(n) = - 20+1760 = 0 Now -20 we X = 88 The critical point is * = 98 ) we check now Whether Plu) has maximum value at n=88 or mininuna Nowo p" (88) = 20 <0. Therefore Plu) has maximum value iat ,x=88 The maxinum value of P(m) is P (88) -10 (88) +1760 X88 - 50000 -77440 + 154 880 - 50000 27440 i Maximum profit = 27440