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# Linear Programming Question

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1. Hi guys, I was doing some D1 practice when I came across this question and was unable to answer it correctly. Any help would really be appreciated!

Q3.
The following figures can be used to compare the three main forms of investment.

Expected Return (Deposits) = 1.5%
Risk Factor (Deposits) = 0

Expected Return (Gilts) = 2.5%
Risk Factor (Gilts) = 20

Expected Return (Deposits) = 8%
Risk Factor (Deposits) = 60

A retired person has £70,000 to invest to supplement their pension. A stockbrocker recommends that they should have a mix of investments to give an expected return of at least 5.5% and an overall risk factor of at most 40. Subject to these constraints, the pensioner wishes to maximise the amount of money in fixed interest investment (gilts).

Let £x,£y,£z be the amounts invested in deposits, gilts and equities respectively, Show that the problem can be formulated as follows.

Maximise y,
subject to x+y+z = 70,000
2x+y>= z (greater than or equal to z)
8x+6y<= 5z (less than or equal to 5z)
2. (Original post by Abstheman)
Hi guys, I was doing some D1 practice when I came across this question and was unable to answer it correctly. Any help would really be appreciated!

Q3.
The following figures can be used to compare the three main forms of investment.

Expected Return (Deposits) = 1.5%
Risk Factor (Deposits) = 0

Expected Return (Gilts) = 2.5%
Risk Factor (Gilts) = 20

Expected Return (Deposits) = 8%
Risk Factor (Deposits) = 60

A retired person has £70,000 to invest to supplement their pension. A stockbrocker recommends that they should have a mix of investments to give an expected return of at least 5.5% and an overall risk factor of at most 40. Subject to these constraints, the pensioner wishes to maximise the amount of money in fixed interest investment (gilts).

Let £x,£y,£z be the amounts invested in deposits, gilts and equities respectively, Show that the problem can be formulated as follows.

Maximise y,
subject to x+y+z = 70,000
2x+y>= z (greater than or equal to z)
8x+6y<= 5z (less than or equal to 5z)
I'll give the one in bold away.

.
3. Thanks!

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