Quick Linear Programming Question

Zakaria007 · #1 $Old$ June 27th, 2009, 01:18 PM

Hey guys,

My question is about linear programming (geometric solution), and I have a bit of trouble understanding the question itself. I tried to solve the problem in many ways, but kept getting a different solution from the answers. The question's a bit long and is about pension funds investment:

Pension Fund Investment A pension fund has decided to invest $45,000 in two high-yield stocks listed in below:

Stock A - Price Per Share: $14 - Yield: 8%
Stock B - Price Per Share: $30 - Yield: 6%

This pension fund has decided to invest at least 25% of the $45,000 in each of the two stocks. *Further, it has been decided that at most 63% of the $45,000 can be invested in either one of the stocks*. How many shares of each stock should be purchased in order to maximize the annual yield, while meeting the stipulated requirements? What is the annual yield in dollars for the optimal investement plan?

Looking at the sentence between the two "*", I understood that I take 63% of the $45,000 and invest in stock A, for instance, so the equation becomes:

if x is the shares in stock A, and y is the shares in stock B, then:
14x <= 28,350

the full equation set is:

14x+30y >= 11,250
14x <=28,350
x>=0, y>=0

and maximizing the profit P:

P = 900x+675y

Thanks guys, and hope to hear from you soon.

CaptainBlack · #2 $Old$ June 28th, 2009, 02:18 AM

Quote:

Originally Posted by Zakaria007 $View Post$

Hey guys,

My question is about linear programming (geometric solution), and I have a bit of trouble understanding the question itself. I tried to solve the problem in many ways, but kept getting a different solution from the answers. The question's a bit long and is about pension funds investment:

Pension Fund Investment A pension fund has decided to invest $45,000 in two high-yield stocks listed in below:

Stock A - Price Per Share: $14 - Yield: 8%
Stock B - Price Per Share: $30 - Yield: 6%

This pension fund has decided to invest at least 25% of the $45,000 in each of the two stocks. *Further, it has been decided that at most 63% of the $45,000 can be invested in either one of the stocks*. How many shares of each stock should be purchased in order to maximize the annual yield, while meeting the stipulated requirements? What is the annual yield in dollars for the optimal investement plan?

Looking at the sentence between the two "*", I understood that I take 63% of the $45,000 and invest in stock A, for instance, so the equation becomes:

if x is the shares in stock A, and y is the shares in stock B, then:
14x <= 28,350

the full equation set is:

14x+30y >= 11,250
14x <=28,350
x>=0, y>=0

and maximizing the profit P:

P = 900x+675y

Thanks guys, and hope to hear from you soon.

You have missed the 65% constaint on B:

$30y \le 28350$

CB