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  • 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 b

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 maximise his returns.

 

 

 

 
 
 
 
 

Answers (1)

Let the investment in bond 'A' and bond 'B' be respectively x and y (in Rs).

To maximize :

z=\left ( \frac{10x}{100}+\frac{9y}{100} \right )  in Rs.

Subject to constraints :

x\geq 0,y\geq 0,x+y\leq 50,000,x\geq 20,000, y\geq 10,000

Corner Points Value of z (in Rs)
A(25000,25000) 4750
B(20000,20000) 3800
C(20000,10000) 2900
D(40000,10000) 4900

So the return is maximum when Rs 40000 are invested in bond 'A' and Rs 10000 are invested in bond 'B'. Also maximum return is Rs 4900.

Posted by

Ravindra Pindel

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