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

Now, the interest on bond A = (x*1*10)/100 = 10x/100

and the interest on bond B = (y*1*9)/100 = 9y/100

Total annual income from interest = 10x/100 + 9y/100

                                                     = 0.1x + 0.09y

Now, given he decides to invest at least 20000 in bond A and at least 10000 in bond B

So, x ≥ 20000 and y ≥ 10000

Again, total investment is x + y and it should not exceed 50000

So, x + y ≤ 50000

Now, the LPP problem is,

Max z = 0.1x + 0.09y

subject to constraints

x + y ≤ 50000

x ≥ 20000, y ≥ 10000

x ≥ y

Now,

        (x, y)                     z =  0.1x + 0.09y

(20000, 10000)                 2950

(40000, 10000)                 4900

(25000, 25000)                 4750

So, when A invest Rs 40000 and B invest Rs 10000, his return is maximum.