OK I have attempted 2 Linear Programming questions and i would like to know if i have got all the equations correct for the first question, and some help on the second one would be much appreciated.

Q1:

A bank is attempting to determine where its assets should be invested during the current year. At present $500 million is available for investment in bonds, home loans, car loans, and personal loans. The annual rate of return on each type of investment is known to be: bonds, 7%; home loans, 8%; car loans, 12%; personal loans, 11%. In order to ensure that the bank’s portfolio is not too risky, the bank’s investment manager has placed the following three restrictions on the bank’s portfolio:

(a) The amount invested in personal loans cannot exceed the amount invested in bonds.

(b) The amount invested in home loans cannot exceed the amount invested in car loans.

(c) No more than 25% of the total amount invested may be in personal loans.

The bank’s objective is to maximize the annual return on its investment portfolio. Formulate an LP (in standard form) that will enable the bank to meet this goal. Assume interest is calculated annually.

My Answer:

Let b=bonds h=home loans c=car loans and p=personal loans

maximise z=0.07b+0.08h+0.12c+0.11p

subject to:

b+h+c+p<=500e6

p<=b

h<=c

p<=125e6

b, h, c, p>=0

(note that 500e6 is 500,000,000 and p<=b means that p i s less than or equal to b)

Q2:

Bulldust Inc. blends silicon and nitrogen to produce two types of fertiliser. Fertiliser 1 must be at least 40% nitrogen and sells for $20/kg. Fertiliser 2 must be at least 70% silicon and sells for $18/kg. Bulldust can purchase up to 800 kg of nitrogen at $10/kg and up to 1000 kg of silicon at $8/kg. Assuming that all fertiliser produced can be sold, formulate an LP to help Bulldust maximize profit.

HELP please =P