Answer to Question #272974 in Math for Thelma 22

Question

d) The Profit function of a firm is of the form π = aQ2 + bQ + c if it is known that π =

31, 34, and 27 when Q = 1, 2, and 3 respectively, write down a set of three unknowns,

a, b, and c. Solve this system to find a, b, and c. hence find the profit when Q = 5. [7]

e) A real estate firm owns the Kasumba Garden Apartments which consists of 90

apartments. At K350 per month every apartment can be rented. However, for each K10

per month increase there will be two vacancies with no possibility of filling them. The

firm wants to receive K31980 per month from rents. What rent should be charged for

each apartment?

Answer 1

d)

$$a(1)^2 + b(1) + c=31$$ $$a(2)^2 + b(2) + c=34$$ $$a(3)^2 + b(3) + c=27$$

$$a + b + c=31$$ $$3a+b=3$$ $$5a+b=-7$$

$$a + b + c=31$$ $$3a+b=3$$ $$2a=-10$$

$$a=-5$$ $$b=18$$ $$c=18$$

$$\pi(Q)=-5Q^2+18Q+18$$

$$\pi (5)=-5(5)^2+18(5)+18=-17$$

e) Let $R=$ revenue.

If the price is $(350+10n)$ then there will be$(90-2n)$ apartments rented.

$$(350+10n)(90-2n)=31980, 0\leq n\leq 45$$

$$31500+200n-20n^2=31980$$

$$20n^2-200n+480=0$$

$$n^2-10n+24=0$$

$$(n-4)(n-6)=0$$

$$n_1=4, n_2=6$$

$$350+10(4)=390$$

$$350+10(6)=410$$

K390 per month or K410 per month.