Question

A retired person wants to invest an amount of Rs 50000.His broker recommends investing in two type of bonds 'A' and 'B' yielding 10% and 9% return respectively on the invested amount.He decides to invest at least Rs 20000 in bond 'A' and at least Rs 10000 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 gis returns.

Answer 1

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