The portfolio manager Ms. Sigma wants to construct an optimal portfolio for an investor. Instead of considering a large number of potential shares to be included in the portfolio, she is planning to consider only five shares from the BSE (1, 2, 3, 4, and 5).

She wishes to develop a flexible L.P. model that can include as many shares as possible. Currently, the investor wants to consider the five shares but he is not sure of the amount he should invest in each share so that he can minimize his risk and at the same time achieve a minimum expected return. Various data for last one year of all five shares have been collected from the stock exchange and are shown in below table. These data can be used by the Sigma to optimize the investment of the investor. Currently investor wishes to invest Rs. 1 lakh in these five shares. Also, the investor wants minimum return of 0.15

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