2. A retired person wants to invest up to an amount of Rs. 30,000 in the fixed income securities. His broker recommends investing in two bonds--- bond A yielding 7% per annum and bond B yielding 10% per annum. After some consideration the person decides to invest at the most Rs. 12,000 in bond B and at least Rs. 6,000 in bond A. He also wants that the amount invested in bond A must be at least equal to the mount invested in bond B. What should the broker recommend if the investor wants to maximise his return on investment: Formulate this as a linear programming problem.
Answers
Answer:
Step-by-step explanation:
Points Z= 7/100 x+ 10/100 y
A(12000,6000) Z=Rs.1440
B(24000,6000) Rs.2280 (Maximize)
C(15000,15000) Rs.2550
D(12000,12000) Rs.2040
Let Rs.x invest in bond A and Rs.y invest in bond B.
Then A.T.P.
Maximise, z= 7/100x+ 10/ 100 y --- (1)
Subject to constraints
x+y≤30,000 --- (a)
x≥12,000---(b)
y≥6,000--- (c)
and x≥y
or x−y≥0--- (d)
and x≥0,y≥0
Now change inequality into equations
x+y=30,000,x=12,000,y=6,000,x=y
Region: put (0, 0) in (a), (b), (c), (d)
0≤30000 (towards origin)
0≥12,000 (away from origin)
0≥6,000 (away from origin)
As shown in the graph.
So from the tabular column, we conclude that he has to invest Rs.24,000 in 'A' and Rs.6,000 in bond 'B' to get maximum return Rs.2280.
Answer: The broker should recommend that his client should invest Rs. 18,000 and Rs. 12,000 to Bonds A and B respectively.
Step-by-step explanation:
(Decision Variables)
Let:
x = Bond A
y = Bond B
(Objective Function)
Maximize: 0.07x + 0.10y
(Constraints)
Subject to:
x + y <= 30000
y <= 12000
x >= 6000
x >= y
x,y >= 0
If we are to graph it, there will be several options which shall be the vertices of the bounded region:
(6000,0)
(6000,6000)
(12000,12000)
(18000,12000)
(30000,0)
If we go back to our objective function and substitute each of these x and y values, the fourth option will have the highest result which is Rs. 2460.
Please comment if you have any corrections for this answer. I hope this answer helps, thank you.