Problema Solution
Julia went on a TV game show and won $32,000. She wants to invest that money, some in a savings account which is relatively safe and some in stocks which is somewhat riskier. Julia wants to put at least $15,000 in savings and at least $10,000 in stocks. The savings account pays 2% and she expects a 6% return on her stocks. Determine how she would invest her money to maximize her return in a single year.
Answer provided by our tutors
let
x = the money invested in savings
y = the money invested in stocks
the constraints are:
x + y <= 32000
x => 15,000
y => 10,100
The objective is: maximize f(x, y) = 0.02*x + 0.06*y
first, lets find the the corner points and the value of f(x,y) in every corner point correspondingly
x + y = 32000
x = 15000
corner point (15000, 17000)
f(x,y) = 0.02*15000 + 0.06*17000 = $1,320
x + y = 32000
y = 10000
corner point (22000, 10000)
f(x,y) = 0.02*22000 + 0.06*10000 = $1,040
x = 15000
y = 10000
f(x,y) = 0.02*15000 + 0.06*10000 = $900
we have that x=15,000 and y=17,000 with the value of the objective function being $1320 maximum value.
Julia should spend $15,000 on savings and $17,000 on stocks with maximum returned $1.320