Question

Qualis Investments is a private limited business that manages personal financial portfolios. The company manages six mutual funds and has a client that has acquired $750,000 from an inheritance. Characteristics of the funds are given in the table below.

	Qualis Mutual Fund Data	Expected Annual Return	Risk Measure
1	Qualis Low-priced Stock Fund	7.23%	11.87
2	Qualis Multinational Fund	8.42%	12.62
3	Qualis Mid-cap Stock Fund	6.66%	13.72
4	Qualis Mortgage Fund	2.72%	3.37
5	Qualis Income Equity Fund	8.89%	8.4
6	Qualis Balanced Fund	3.50%	6.91

The company recommends that no more than $300,000 be invested in any individual fund, and that at least $80,000 be invested in each of the mid-cap stock and mortgage fund. The total amount invested in the low-priced and multinational funds are at least 35% of the total investment. The client would like an average return on investment of at least 6%. Assume that ^X₁ through ^X₆ represents the dollar amount invested in funds 1 through 6, respectively.

Which of the following is the correct constraint for the return on investment?

Group of answer choices

(7.23 ^X₁ +8.42 ^X₂ +6.66 ^X₃ + 2.72 ^X₄ + 8.89 ^X₅+ 3.5 ^X₆) ≥ 0.06

(0.0723 ^X₁ +0.0842 ^X₂ +0.0666 ^X₃ + 0.0272 ^X₄ + 0.0889 ^X₅+ 0.035 ^X₆) ≥ 0.06

(7.23 ^X₁ +8.42 ^X₂ +6.66 ^X₃ + 2.72 ^X₄+ 8.89 ^X₅+ 3.5 ^X₆) ≥ 0.06 (750,000)

(0.0723 ^X₁ +0.0842 ^X₂ +0.0666 ^X₃ + 0.0272 ^X₄+ 0.0889 ^X₅+ 0.035 ^X₆) ≥ 0.06(750,000)

Answer 1

Here the total investment is $750,000

The client would like an average return on investment of at least 6%

So the client would like an return on investment as 0.06 * 750,000 since he likes to make at least 6%

Assume that ^X₁ through ^X₆ represents the dollar amount invested in funds 1 through 6, respectively

We multiply the average returns of each fund with the dollar amount invested in each fund to find the return on investment

so return on investment is

0.0723 ^X₁ +0.0842 ^X₂ +0.0666 ^X₃ + 0.0272 ^X₄+ 0.0889 ^X₅+ 0.035 ^X₆

Expected Annual return are given in % so they should be divided by 100

But the return on investment should be atleast 0.06 * 750,000

So constraint for the return on investment is

0.0723 ^X₁ +0.0842 ^X₂ +0.0666 ^X₃ + 0.0272 ^X₄+ 0.0889 ^X₅+ 0.035 ^X₆  ≥ 0.06(750,000)

So Answer is Option D