Q. 145.0( 2 Votes )

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]

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,


(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.


Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Range of Quadratic/quadratic & linear/Linear functionsRange of Quadratic/quadratic & linear/Linear functionsRange of Quadratic/quadratic & linear/Linear functions45 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
caricature
view all courses
RELATED QUESTIONS :