An investment club has set a goal of earning 15% on the money they invest in sto

Question

An investment club has set a goal of earning 15% on the money they invest in stocks. The members are considering purchasing three possible stocks, with their cost per share (in dol lars) and their projected growth per share (in dollars) summarized in the table. (Let x-computer shares, y - utility shares, and z - retail shares.) Stocks Computer (x) Utility (y) Retail (z) Cost/share 30 26 2.40 (a) If they have $392,000 to invest, how many shares of each stock should they buy Growth/share6.00 6.00 to meet their goal? (If there are infinitely many solutions, express your answers in terms of z as in Example 3.) (b) If they buy 1200 shares of retail stock, how many shares of the other stocks do they buy? computer utility shares shares What if they buy 2400 shares of retail stock? computer utility shares shares (c) What is the minimum number of shares of computer stock they will buy? shares What is the number of shares of the other stocks in this case? utility retail shares shares (d) What is the maximum number of shares of computer stock purchased? shares

Explanation / Answer

a) There are infinate solutions to that No of Share in terms of z= $392000/cost per share of z 392000/26 15076 Stocks b) if we buy 1200 stocks of retail stock so total amount spended 1200*26 $31200 Amount left $392000-$31200=360800 So we will buy shares for both computer(Since same growth but low cost) So, $360800/30 12026 c) If we buy 2400 shares of retail stock, then value left $392000-2400*26 $329600 No of computer stocks =$329600/30 10986 d) Max no of shares computer stock can purchase 392000/30 13066

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