A retired person

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,

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