Q24 of 118 Page 31

Anil wants to invest at most ₹ 12000 in Saving Certificates and National Saving Bonds. According to rules, he has to invest at least ₹ 2000 in Saving Certificates and at least 4000 in National Saving Bonds. If the rate of interest on saving certificate is 8% per annum and the rate of interest on National Saving Bonds is 10% per annum, how much money should he invest to earn

maximum yearly income? Find also his maximum yearly income.

Let Anil invests Rs x and Rs y in saving certificate (SC) and National saving bond (NSB) respectively.


Since, the rate of interest on SC is 8% annual and on NSB is 10% annual. So, interest on Rs x of SC is and Rs y of NSB is per annum.


Let Z be total interest earned so,


Z = +


Given he wants to invest Rs 12000 is total


x + y 12000


According to the rules he has to invest at least Rs 2000 in SC and at least Rs 4000 in NSB.


x 2000


y 4000


Hence the mathematical formulation of LPP is to find x and y which


Maximizes Z


Max Z = +


Subject to constraints


x 2000


y 4000


x + y 12000


x,y 0


The region represented by x 2000: line x = 2000 is parallel to the y - axis and passes through (2000,0).


The region not containing the origin represents x 2000


As (0,0) doesn’t satisfy the inequation x 2000


The region represented by y 4000: line y = 4000 is parallel to the x - axis and passes through (0,4000).


The region not containing the origin represents y 4000


As (0,0) doesn’t satisfy the inequation y 4000


Region represented by x + y 12000: line x + y = 12000 meets axes at A(12000,0) and B(0,12000) respectively. The region which contains the origin represents the solution set of x + y 12000


as (0,0) satisfies the inequality x + y 12000.


Region x,y 0 is represented by the first quadrant.


24.jpg


The corner points are E(2000,10000), C(2000,4000), D(8000,4000).


The values of Z at these corner points are as follows:



The maximum value of Z is Rs 1160 which is attained at E(2000,10000).


Thus the maximum earning is Rs1160 obtained when Rs 2000 were invested in SC and Rs 10000 in NSB.


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