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  • Explain solution RD Sharma class 12 Chapter 29 Linear Programming exercise 29.4 question 24

Explain solution RD Sharma class 12 Chapter 29 Linear Programming exercise 29.4 question 24

Answers (1)

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 \frac{8 x}{100} and Rs.y of NSB is \frac{10 x}{100} per annum.

Let Z be total interest earned so,

                                  Z=\frac{8 x}{100}+\frac{10 x}{100}

Given he wants to invest Rs.12000 is total

                                  x+y \leq 12000

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

                                  \begin{aligned} &x \geq 2000 \\ &y \geq 4000 \\ &x+y \leq 12000 \\ &x, y \geq 0 \end{aligned}

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

The region which does not contains origin represents x \geq 2000  as (0,0) doesn’t satisfy the in equation x \geq 2000

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

The region which does not contains origin represents y \geq 4000  as (0,0) doesn’t satisfy the in equation y \geq 4000

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

Region x, y \geq 0 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

z=\frac{8 x}{100}+\frac{10 x}{100}

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.

 

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