An investment broker wants to invest up to dollar-sign 28 comma 000 point She can invest in two mutual funds based on their yearly average return for the 5 years ending December 31, 2009: the Franklin Natural Resources fund yielding 7 % and the Oppenheimer Developing Markets A fund yielding 13 % Baseline Number . She wants to invest at least dollar-sign 7000 in the Franklin Natural Resources fund and no more than dollar-sign 11,000 in the Oppenheimer Developing Markets A fund. How much should she invest in each type of fund to maximize her return?

$2,970

Explanation:

An investor has $28,000 to invest between two funds:

If she wants to maximize her returns, then she should invest as much as possible in the second fund. She is willing to invest:

let F = amount invested in Franklin

let O = amount invested in Oppenheimer

F + O = 33,000

F ≥ 7,000

O ≥ 11,000

MAX return = 0.07F + 0.13O

O = 11,000 (yields higher return)

F + 11,000 = 33,000

F = 22,000

MAX return = 0.07(22,000) + 0.13(11,000) = $1,540 + $1,430 = $2,970

bd = 9 cm

step-by-step explanation:

in a 30°-60°-90° triangle, the ratio of side lengths is 1 : √3 : 2. that is, the longest side (hypotenuse) is twice the length of the shortest side.

all of the triangles in your geometry are 30°-60°-90° triangles. ac is the hypotenuse of δacd, and the short side of δabc.

the short side ad of δacd will be half the length of ac, so 3 cm. the hypotenuse ab of δabc will be twice the length of ac, so 12 cm. segment bd is the difference of the lengths ab and ad, so is

bd = ab -ad

bd = 12 cm - 3 cm = 9 cm

comment on side length ratios

you can figure the ratios of side lengths in a 30°-60°-90° triangle by considering the trig ratios of the angles. or you can figure the length of the altitude of an equilateral triangle of side length 2 using the pythagorean theorem.

answer; 33,000;