Explain solution RD Sharma class 12 Chapter 29 Linear Programming exercise 29.4 question 24
Answer:
Maximum Earning Rs.1160 when Rs.2000 was invested in SC and Rs.10000 in NSB
Hint:
Form Linear Equation and solve graphically.
Given:
Anil wants to invest at most Rs.12000 in saving certificates and National saving Bonds. According to rules, he has to invest at least Rs.2000 in saving certificate and at least Rs.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 Bond is 10% per annum.
Solution:
Let Anil invests Rsx and Rs.y in saving certificate (SC) and National Saving Band (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,
Given he wants to invest Rs.12000 is total
According to the rules he has to invest at least Rs.2000 in SC and at least Rs.4000 in NSB
Region represented by : the line x=2000 is parallel to the y-axis and passes through (2000,0).
The region which does not contains origin represents as (0,0) doesn’t satisfy the in equation
Region represented by : the line y=4000 is parallel to the x-axis and passes through (0,4000).
The region which does not contains origin represents as (0,0) doesn’t satisfy the in equation
Region represented by : the line meets axes at A(12000,0) and B(0,12000)respectively. The region which contains origin represents the solution set of as (0,0) satisfies the in equation
Region is represented by the first quadrant.
Scale: On x-axis, 1 Big Division=2000 units
On y-axis, 1 Big Division=2000 units
The corner points are E(2000,10000), C(2000,4000),D(8000,4000)
The values of Z at these corner points are as follows
Corner Points |
|
O |
0 |
E |
1160 |
D |
1040 |
C |
560 |
The maximum value of Z is rs.1160 which is attained at E(2000,10000)
Thus the maximum earning is Rs.1160 obtained when Rs.2000 were invested in SC and Rs.10000 in NSB.