Question

AntiFam, a hunger-relief organization, has earmarked between $2 million and $2.5 million (inclusive) for aid to two African countries, Country A and Country B. Country A is to receive between $1 millionand $1.5 million (inclusive), and Country B is to receive at least $0.75 million. It has been estimated that each dollar spent in Country A will yield an effective return of $0.40, whereas a dollar spent in Country B will yield an effective return of $0.90. 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 (in millions of dollars) to be given to Country A and Country B, respectively, then the objective function to be maximized is

P = 0.4x + 0.9y.

(x, y)

=

What is the optimal return?

$   million

AntiFam, a hunger-relief organization, has earmarked between $2 million and $2.5 million (inclusive) for aid to two African countries, Country A and Country B. Country A is to receive between $1 millionand $1.5 million (inclusive), and Country B is to receive at least $0.75 million. It has been estimated that each dollar spent in Country A will yield an effective return of $0.40, whereas a dollar spent in Country B will yield an effective return of $0.90. 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 (in millions of dollars) to be given to Country A and Country B, respectively, then the objective function to be maximized is

P = 0.4x + 0.9y.

(x, y)

=

What is the optimal return?

$   million

Answer 1

y = Amount money x= Amount of money invested in Country A of invested in Country B objective function: Manimize. I=0.4n tory - P Constraints are: 25nty & 3.5 lans 1.75 xty 23.5 (0,3,5) 4 (365,0) nty 22 • (62) 4 (20) y 0.25 0,215) 12 (175, 1.75) y=0.25 (1-75,0.25 Q T 3 2 4 - 4 - 3 -2 nty=2 xty=3,5 X=1 x=1.75 -3 - 4 aty=2 x= aty=3.5 x = 1 soling, solving there two, we get x=7 y=1 * xty = 3.5 a=1.75 xty = 2 y = 0.25 solving these two, we get solving n=1.75 2=1.75 y=0.25 y=1.75

p=z=0.4x + bay N Coordinated (1,1) 1.3 (1-75,0:25) 0.925 (0,2.5) (3.25 (1.75, 1.75) 2.275 Thus at (1, 2.5) , value of r is manimum. .. Optimal return in (n.) (1,2.5)