xeneration9
02-22-2007, 04:17 AM
Im trying to solve this question, but Im really havng hard time to find answer.
Could anybody help this two questions?
#15 A hunger-relief organization, has earmarked between $2 and $2.5
million, inclusive, for aid to two African countries, country A and
country B. Country A is to receive between $1 and $1.5 million,
inclusive, in aid, and country B is to receive at least $0.75 million
in aid. It has been estimated that each dollar spent in country A will
yield an effective return of $.85, whereas a dollar spent in country B
will yield an effective return of $.80. How should the aid be allocated
if the money is to be utilized most effectively according to these
criteria? (Hint: If x and y denote the amount of money to be given to
country A and country B, respectively, then the objective function to
be maximized is P = 0.85x + 0.8y.)
________ million to country A and ________ million to country
B
The variables were identified, as well as the objective function. The
constraints are:
x + y >= 2
x + y <= 2.5 (between 2 and 2.5 million)
x >= 1
x <= 1.5 (country A receives between 1 and 1.5 million)
y >= .75 (country B receives at least .75 million)
Then solve by Method of Corners
#15 Patricia has at most $22,000 to invest in securities in the form
of corporate stocks. She has narrowed her choices to two groups of
stocks: growth stocks that she assumes will yield a 15% return
(dividends and capital appreciation) within a year and speculative
stocks that she assumes will yield a 24% return (mainly in capital
appreciation) within a year. Determine how much she should invest in
each group of stocks in order to maximize the return on her investments
within a year if she has decided to invest at least 3 times as much in
growth stocks as in speculative stocks.
________ in growth stocks and ________ in speculative stocks
maximum return: ________
x = amount invested in growth stocks
y = amount invested in speculative stocks
Maximize
R = .15x + .24y (maximize return)
Subject to
x + y <= 22000 (at most $22,000 to invest)
y >= 3x (at least 3 times as much in growth stocks as in speculative
stocks)
x>=0, x>=0 (can't invest a negative amount)
Could anybody help this two questions?
#15 A hunger-relief organization, has earmarked between $2 and $2.5
million, inclusive, for aid to two African countries, country A and
country B. Country A is to receive between $1 and $1.5 million,
inclusive, in aid, and country B is to receive at least $0.75 million
in aid. It has been estimated that each dollar spent in country A will
yield an effective return of $.85, whereas a dollar spent in country B
will yield an effective return of $.80. How should the aid be allocated
if the money is to be utilized most effectively according to these
criteria? (Hint: If x and y denote the amount of money to be given to
country A and country B, respectively, then the objective function to
be maximized is P = 0.85x + 0.8y.)
________ million to country A and ________ million to country
B
The variables were identified, as well as the objective function. The
constraints are:
x + y >= 2
x + y <= 2.5 (between 2 and 2.5 million)
x >= 1
x <= 1.5 (country A receives between 1 and 1.5 million)
y >= .75 (country B receives at least .75 million)
Then solve by Method of Corners
#15 Patricia has at most $22,000 to invest in securities in the form
of corporate stocks. She has narrowed her choices to two groups of
stocks: growth stocks that she assumes will yield a 15% return
(dividends and capital appreciation) within a year and speculative
stocks that she assumes will yield a 24% return (mainly in capital
appreciation) within a year. Determine how much she should invest in
each group of stocks in order to maximize the return on her investments
within a year if she has decided to invest at least 3 times as much in
growth stocks as in speculative stocks.
________ in growth stocks and ________ in speculative stocks
maximum return: ________
x = amount invested in growth stocks
y = amount invested in speculative stocks
Maximize
R = .15x + .24y (maximize return)
Subject to
x + y <= 22000 (at most $22,000 to invest)
y >= 3x (at least 3 times as much in growth stocks as in speculative
stocks)
x>=0, x>=0 (can't invest a negative amount)