Q. 255.0( 1 Vote )

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.

Answer :

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.


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