Use the provided template file that has the annual expected return for each stock and the annual variance$-$covariance matrix, choose some random initial values for the weight in each stock $($make sure all the weights sum up to $1)$ and use the returns, variance$-$covariance matrix and the weights to calculate portfolio expected return, portfolio variance and portfolio standard deviation $($using the matrix formulas in class$).$

a$)$ Use solver to find the minimum variance portfolio of these stocks that offers a return of at least $5\%.$ Assume short sales are not allowed. What is the optimal portfolio? How much do you invest in each stock? What is the expected portfolio return and variance?

b$)$ Use solver to find the minimum variance portfolio of these stocks that offers a return of at least $5\%.$ Assume short sales are allowed. What is the optimal portfolio? How much do you invest in each stock? What is the expected portfolio return and variance?

c$)$ Assume that you are trying to solve again part a but now there is an additional constraint.