suppose you have $16,000 to invest in three stocks, a, b, and c. stock a is a low - risk stock that has…

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. stock a: x≥ stock b: y≥ and y≤ x stock c: 16 - x - y≥ 16 - x - y≤ 16 - x - y≤ x done

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. stock a: x≥ stock b: y≥ and y≤ x stock c: 16 - x - y≥ 16 - x - y≤ 16 - x - y≤ x done

Answer

Explanation:

Step1: Analyze investment - at - least condition

You want to invest at least $1000 in each stock. For stock A with investment amount $x$, we have $x\geq1000$. For stock B with investment amount $y$, we have $y\geq1000$. For stock C, the investment amount is $z = 16000 - x - y$, so $16 - x - y\geq1000$ (where the amounts are in thousands of dollars).

Step2: Analyze investment - limit in stock C

You decide to invest no more than $7000 in stock C, so $16 - x - y\leq7$.

Step3: Analyze relationship between C and A

The amount invested in C is less than 4 times the amount invested in A, so $16 - x - y<4x$, or $16 - x - y\leq4x$.

Step4: Analyze relationship between B and A

You invest less than twice as much in stock B as in stock A, so $y < 2x$, or $y\leq2x$.

Answer:

Stock A: $x\geq1000$ Stock B: $y\geq1000$ and $y\leq2x$ Stock C: $16 - x - y\geq1000$ $16 - x - y\leq7$ $16 - x - y\leq4x$