In a portfolio problem, X1, X2, and X3 represent the number of shares purchased of stocks 1, 2, and 3, which have selling prices of $15, $47.25, and $110, respectively. The investor has up to $50,000 to invest.
-The investor stipulates that stock 1 must not account for more than 35% of the number of shares purchased. Which constraint is correct?
A) X1 ? 0.35
B) X1 = 0.35 (50000)
C) X1 ? 0.35(X1 + X2 + X3)
D) X1 = 0.35(X1 + X2 + X3)

Question

Quizplus · Accepted Answer

We know that the total amount to be invested is $50,000. Let X1, X2, and X3 be the number of shares purchased for the three stocks. The selling price of the three stocks are $15, $47.25, and $110 respectively.

So, the cost of buying X1 shares of Stock 1 at $15 per share is 15X1. Similarly, the cost of buying X2 shares of Stock 2 at $47.25 per share is 47.25X2 and the cost of buying X3 shares of Stock 3 at $110 per share is 110X3.

The total amount invested should not exceed $50,000. Hence, we can write the first constraint as:

15X1 + 47.25X2 + 110X3 ≤ 50,000

We are also given that Stock 1 should not account for more than 35% of the total number of shares purchased (i.e., X1/(X1+X2+X3) ≤ 0.35). We can write this as:

X1 ≤ 0.35(X1+X2+X3)

This means that the number of shares of Stock 1 should be less than or equal to 35% of the total number of shares purchased.

Therefore, the correct constraint is C: X1 ≤ 0.35(X1+X2+X3).

In a Portfolio Problem, X1, X2, and X3 Represent the Number