1. TanFin12 3.2.027·CMI Formulate but do not solve the following exercise as a l

Question

1. TanFin12 3.2.027·CMI Formulate but do not solve the following exercise as a linear programming problem. Ashley has earmarked at most $230,000 for investment in three mutual funds: dollars in a money market fund, y dollars in an international equity fund, and z dollars in a growth-and-income fund. The money market fund has a rate of return of 6%/year, the international equity fund has a rate of return of 10%/year, and the growth-and-income fund has a rate of return of 15%/year, Ashley has stipulated that no more than 20% of her total portfolio should be in the growth-and-income fund and that no more than 45% of her total portfolio should be in the international equity fund. To maximize the return on her investment P (in dollars), how much should Ashley invest in each type of fund? Maximize a subject to the constraints 2000 total investments growth-and-income percentage | international equity percentage 20 20 20 x 2 0

Explanation / Answer

let x dollars in money market fund y dollars in interational equity fund

z dollars in growth income fund

given total investment =230,000

x+y+z<=230,000

given market fund has return 6% international equity fund 10% and growth -income fund 15% p =0.06x+0.1y+0.15z=(3/50)x+(1/10)y+(3/20)

given

not more than 20% of her portfolio should be in growth and income fund

z<=20%(x+y+z)

z<=(1/5)(x+y+z)

-(1/5)x-(1/5)y+4/5z<=0

and given not more than 45% of portfollo in international equity fund

y<=0.45(x+y+z)

-(9/20)x+(11/20)y-(9/20)z<=0

maximize P= (3/50)x+(1/10)y+(3/20)

subjected to

x+y+z<=23000

-(1/5)x-(1/5)y+4/5z<=0

-(9/20)x+(11/20)y-(9/20)z<=0

x>=0

y>=0

z>=0

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