Question

In a Portfolio Selection problem, let X1, X2 and 3 represent the number of shares purchased for stocks 1, 2 and 3, which have selling prices of $45, $15 and $100 respectively. The returns on investment for stocks 1, 2 and 3 are 10%, 8%, and 13% of the amount of money invested respectively The investor has up to $40,000 to invest. One appropriate constraint would be: Select one: O a. 45x1 + 15x2 + 100x3 s 40,000; O b. 15x1 + 45x2 + 100x3 = 40,000; O c. X1 + x2 + x3 s 40,000; O d. 0.08)(15)X1 + (-10) (45)x2 + (.13) (100)x3 s 40,000. For the Portfolio Selection problem, the number of shares of stock 1 must be at most 35% of the total number of shares purchased. One appropriate constraint would be: Select one: O a..65, - .35x2 - 135x3 5.35; O b. 65x1 - .35x2 - 35x3 = 0; O c. 65x1 - 35x2 - 35x3 = 0; O d. X1 (.35)(x1 + x2).

Answer 1

Q-1) As $x_1=\text{number of shares of stock 1 which cost 45}$ ,

$x_2=\text{number of shares of stock 2 which cost 15}$ , $x_3=\text{number of shares of stock 3 which cost 100}$

So total amount spend on these three stocks is $45x_1+15x_2+100x_3$

As the investor has only 40,000 to invest

So we must have $45x_1+15x_2+100x_3 \leq 40000$

Option a. is correct

Q-2) Total number of shares possible is $x_1+x_2+x_3$

Since its given that $x_1$ is at most 35% of the total so

$x_1 \leq 0.35(x_1+x_2+x_3) \\ \Rightarrow (1-0.35)x_1-0.35x_2-0.35x_3 \leq 0$

Or $0.65x_1-0.35x_2-0.35x_3 \leq 0$

Thus, Option b. is correct

Q-3) As $x_2=\text{number of shares of stock 2 which cost 15}$ and at least 1000 is to be invested into it so $15x_2 \geq 1000$ . Also

Number of shares of stock 2 and 3 is at least 350 so $x_2+x_3 \geq 350$

So we have the constraint as

$15x_2 \geq 1000$   and $x_2+x_3 \geq 350$

Option a. is correct