# A retired person wants to invest an amount of ₹ 50,000. His broker recommends investing in two types of bonds ‘A’ and ‘B’ yielding 10% and 9% return respectively on the invested amount. He decides to invest at least ₹ 20,000 in bond ‘A’ and at least ₹ 10,000 in bond ‘B’. He also wants to invest at least as much in bond ‘A’ as in bond ‘B’. Solve this linear programming problem graphically to maximize his returns. [CBSE 2016]

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.

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