An investment firm hired you to manage one of their new mutual funds. The fund invests in two main companies/stocks, Pittsburg Steel (X_1) and IMB(X_2). Pittsburg Steel is currently trading at exist40.00 per share and IMB at exist30.00 per share. Your goal is to maximize the return on investment (ROI) for the initial investment period. Recent market analysis indicates that both companies will be trading higher at the end of this investment period. Pittsburg Steel's projected return (ROI) is expected to be exist10.00 per share and IMB's projected return (ROI) is expected to be exist15.00 per share for the initial investment period. The firm gives you exist50,000 as an initial investment to get your fund going but stipulates that at least 400 shares of each stock must be purchased. Additionally your initial research shows that IMB is a higher risk alternative and you decide that no more than 1/2 of the total number of shares purchased should be invested in IMB

a) Formulate this LP model to determine the number of shares you should purchase of each stock to maximize the total ROI for the initial investment period. Write in standard form.