In the past, the client invested in two different types of stocks: high tech stocks and pharmaceutical stocks. He needs to decide how many units of each type he should keep this year. He has a budget to invest up to £1.5 million. He has decided that, independently from his decision on the other stocks, he will invest £100000 in the most profitable stocks between ‘Pippo’ and ‘Paperino’. On the other end, each unit of the high tech stocks costs £60 and provides an annual rate of return of 10%; each unit of pharmaceutical stocks £100 and provides an annual rate of return of 4%.

The client wants to minimise the diversification of the portfolio. He requires that the annual income from the investments will be at least £70000. He has calculated a diversification investment measure. Each unit invested in high tech stocks has a diversification index of 7. Each unit invested in the pharmaceutical stocks has a diversification index of 3, because it has a smaller range of assets. The client has also specified that at least £300000 should be invested in the high tech stocks.

F. The client wants to know how many units of each type of investments he should purchase to minimise the total diversity index for the portfolio. Formulate a linear programming model for this problem .