Jorge has decided to invest at most $130,000 in securities in the form of corpor

Question

Jorge has decided to invest at most $130,000 in securities in the form of corporate stocks. He has classified his options into three groups of stocks: bluechip stocks that he assumes will yield a 10% return (dividends and capital appreciation) within a year, growth stocks that he assumes will yield a 15% return within a year, and speculative stocks that he assumes will yield a 20% return (mainly due to capital appreciation) within a year. Because of the relative risks involved in his investment, Jorge has further decided that no more than 30% of his investment should be in growth and speculative stocks and at least 50% of his investment should be in blue-chip and speculative stocks. Determine how much Jorge should invest in each group of stocks in the hope of maximizing the return on his investments.

Explanation / Answer

let invest ment in blue chip = x

and invest ment in growth is = y

invest ment in speculative = z

we Know that x+z>50%of 130,000

       and z+ y<30% of 130,000

x+y+z = 130,000

(x+z) + y = 130,000

0.5*130,000 +y < 130,000

y<0.5*130,000

similarly

x+0.3*130,000>130,000

x>0.7*130,000

now

1.1*x+1.15*y+(130,000-x-y)1.2 = return

2x- y = some constant

maximise this difference to get maximum return

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