A retired person wants to invest an amount of Rs. 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 Rs. 20,000 in bond 'A' and at least Rs. 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: Max return = Rs 4900 at (40000, 10000): Rs 40,000 in bond A and Rs 10,000 in bond B
Solution
Let Rs x be invested in bond A and Rs y in bond B. Return to maximise: Z=0.10x+0.09y. Total: x+y≤50000 x≥20000, y≥10000, x≥y Corner points of the feasible region: (20000,10000), (40000,10000), (25000,25000) (intersection of x=y and x+y=50000) and (20000,20000) (intersection of x=20000 and x=y). Evaluate Z=0.10x+0.09y: (20000,10000): Z=2900 (40000,10000): Z=4000+900=4900 ← maximum (25000,25000): Z=4750 (20000,20000): Z=3800
∴Zmax=Rs 4900 at (40000,10000)
He should invest Rs 40,000 in bond A and Rs 10,000 in bond B for a maximum return of Rs 4900.Feasible region for the bond investment problem, with corner points (20000, 10000), (40000, 10000), (25000, 25000) and (20000, 20000).
