7. A person wants to invest at most Rs. 18,000 in Bonds A and B. According to the rules, he has to

invest at least Rs. 4,000 in Bond A and at least Rs. 5,000 in Bond B. If the rate of interest on bond A is

9 % per annum and the rate of interest on bond B is 11 % per annum , how much money should he

invest to earn maximum yearly income ?

Let person invest Rs. x in bond A and Rs. y in bond B.

Then, interest on two bonds is , that is,

Bond A =

and 

Bond B =

Total annual income from interest =

Also, Since he should at least invest Rs. 4000 in bond A and Rs.5000 in bond B .

∴x≥4000  and  y≥5000

Again, since total investment is (x+y) bonds should not exceed Rs. 18000

∴x+y≤18000

So, the  L.P. problem is 

Max Z=0.09x+0.11y

subject to constraints

x+y≤18000

x≥4000

y≥5000

x≥0  ,y≥0