Exercise $2$

Suppose a company has $$2,000,000$ to invest in three different financial instruments: Stock A$,$ Stock B$,$ and Stock C$.$ The expected returns and risk $($standard deviation$)$ for each investment are given in the table below:

Expected Return Risk $($Standard Deviation$)$

Stock A $0\mathrm{.}09$

Stock B $0\mathrm{.}22$

Stock C $0\mathrm{.}07$

Let $x1,x2,$ and $x3$ represent the amount of money invested in Stock A$,$ Stock B$,$ and Stock $C,$ respectively. The goal is to maximize the expected return while keeping the total investment amount within the available budget.

In addition to the budget constraint, let's consider constraints on the minimum and maximum investment in each financial instrument. Suppose there are the following constraints:

Budget Constraint: $x1+x2+x3=2,000,000$

Minimum Investment Constraint for Stock A:

The company wants to invest at least $$500,000$ in Stock A$.$

Minimum and Maximum Investment Constraints for Stock B:

The company wants to invest between $$100,000$ and $$300,000$ in Stock B

Minimum and Maximum Investment Constraints for Stock C:

The company wants to invest between $$200,000$ and $$400,000$ in Stock $C$

Define the decision variables, objective function, and constraints.

Formulate this problem as a Linear Program problem and use MS Excel's Solver to find a solution to the following questions:

Questions

What is the maximum return found by the Solver?

What is the maximum allocation of funds for Stock A found by the Solver?

What is the maximum allocation of funds for Stock B found by the Solver?

What is the maximum allocation of funds for Stock $C$ found by the Solver?