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 dollars) and their projected growth per share (in dollars) summarized in the table. (Let x = computer shares, y = utility shares, and z = retail shares.) If they have $392,000 to invest, how many shares of each stock should they buy to meet their goal? (If there are infinitely many solutions, express your answers in terms of z as in Example 3.) (x, y, z) = (0.6z + 2800, 700 - z, z) If they buy 1200 shares of retail stock, how many shares of the other stocks do they buy? computer _______ shares utility _______ shares What If they buy 2400 shares of retail stock? computer _______ shares utility _______ shares 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 _______ shares retail _______ shares What is the maximum number of shares of computer stock purchased? _______ shares What is the number of shares of the other stocks in this case? utility _______ shares retail _______ shares

Explanation / Answer

Well, Part (a) you have already done.

(b) Number of shares in retail z = 1200, then we have

Computer Shares x = 0.6 z + 2800 = 0.6 x 1200 + 2800 = 3520, and

Utility Shares y = 7000 - 1200 = 5800

If Number of shares in retail z = 2400, then we have

Computer Shares x = 0.6 z + 2800 = 0.6 x 2400 + 2800 = 4240, and

Utility Shares y = 7000 - 2400 = 4600

(c) The minimum will be computer stack (x) when z (the retail stack) = 0,

Therefore,  xmin = 2800, and

Utility Shares y = 7000 - 0 = 7000, and

Retail Shares z = 0

(d) The maximum will be computer stack (x) when z (the retail stack) is maximum= 7000, (Since y can not be negative)

Therefore,  xmax = 0.6 z + 2800 = 0.6 x 7000 + 2800 = 7000,

Utility Shares y = 7000 - 7000 = 0, and

Retail Shares z = 7000

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