Question

Suppose you have $16,000 to invest in three stocks, A, B, and C. Stock A is a low-risk stock that has expected returns of 4%. Stock B is a medium-risk stock that has expected returns of 5%. Stock C is a high-risk stock that has expected returns of 6%. You want to invest at least $1,000 in each stock. To balance the risks, you decide to invest no more than $7,000 in stock C and to limit the amount invested in C to less than 4 times the amount invested in stock A. You also decide to invest less than twice as much in stock B as in stock A. How much should you invest in each stock to maximize your expected profit? Complete the constraints.

Answer 1

To maximize expected profit, you need to determine the amount to invest in stocks A, B, and C while considering the given constraints.

Step-by-step explanation:

To invest in each stock to maximize expected profit, we need to determine the amount to invest in stocks A, B, and C while considering the given constraints.

Let's denote the amount invested in stock A as x, in stock B as y, and in stock C as z.

The constraints are as follows:

• At least $1,000 should be invested in each stock: x > $1,000, y > $1,000, z > $1,000
• No more than $7,000 should be invested in stock C: z < $7,000
• The amount invested in C should be less than 4 times the amount invested in A: z < 4x
• The amount invested in B should be less than twice the amount invested in A: y < 2x

To maximize expected profit, we need to maximize the sum of the expected returns from each stock:

Expected profit = 0.04x + 0.05y + 0.06z

By solving the constraints and optimizing the expected profit function, we can find the optimal values for x, y, and z.

Answer 2

Stock A: 1

Stock B: 1 and y=2

Stock C: 1, 7, 4