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

Question

An investment club has set a goal of earming 15% on the money they invest in stocks. The members are considering Purchasing three possible stocks, with their cost per share (n dollars) and their projected growth per share (n dollars) summarized in the table. (Let computer shares, utility shares, and z Computer (x) Utility Cy) Retail (z) Cost share Growth/share 6.00 6.00 2.40 (a) If they have s392,000 to invest, how many shares of each stockshould they buy to meet their goal? (If there are infintely many solutions, express your answers in terms of z as in (b) If they buy 1200 shares of retail stock, how many shares of the other stocks dothey buy? what if they buy 2400 shares of retail stock? computer stock they will buy? (c) What is the minimum number of shares of What is the number of shares of the other stocks in this case? computer stock purchased? (d) what is the maximum number of shares of of shares of the other stocks in this case?

Explanation / Answer

Given

total money =392000;

x = computer share;

y=utility sharel

z= retail share;

total cost of shares is

c = 30x+44y+26z<=392000;

now;profit on each stock we have;

P=(6x+6y+2.4z)/(30x+44y+26z)>=0.15;

=> 1.5x-0.6y-1.5z>=0;

we get;

1.5x=0.6y+1.5z;

x=0.4y+z;

30(0.4y+z)+44y+26z=392000;

12y+30z+44y+26z=392000;

56y+56z=392000;

y+z=7000;

y=7000-z;

x=0.4(7000-z)+z=2800-0.4z+z=2800+0.6z;

we get;

{x,y,z}={2800+0.6z,7000-z,z};

b)1200 retail stocks;

computer shares;

2800+0.6*1200=3520 shares;

utility shares= 7000-1200=5800shares;

c) 2400 retail shares;

computer shares=2800+0.6*2400=4240;

utility shares=7000-2400=4600

d) minimum computer stocks = 2800;

utility stocks =7000, retail stocks = 0;

e) maximum number of shares of computer stock when z is maximum;

7000-z>0; z <=7000;

z=7000;

maximum number of computer stocks = 2800+0.6*7000=7000;

utility stock=0;

retail stock = 7000;

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