Question

David wants to invest at most $Rs.12,000$ in bonds $A$ and $B$. According to the rule, he has to invest at least $Rs.2,000$ in Bond $A$ and at least $Rs.4,000$ in Bond $B$. If the rates of interest on Bonds $A$ and $B$ respectively are $8\%$ and $10\%$ perannum, formulate the problem as L.P.P. and solve it graphically for maximum interest. Also determine the maximum interest received in a year.

Answer 1

Let David invested $Rsx$ & $Rsy$ in Bond $A$ & Bond $B$ resp

Rate of interest on Bond $A=8\%/annum$

$B=10\%/annum$

Interest on Bond $A=x8/100$

$=Rs2x/25$

$B=y10/100$

$=Rsy/10$

Total Interest $=Rs\frac{2x}{25}+\frac{y}{10}$

$z=\frac{2x}{25}+\frac{y}{10}$

Constants: $x+y\le 12,000$

$x\ge 2000$

$y\ge 4000$

$A(2000,4000);B(8000,4000)$

$C(2000,10000)$

at $A$

$Z=\frac{2\left(2000\right)}{25}+\frac{4000}{10}=160+400=560$

at $B$

$z=\frac{2\left(8000\right)}{25}+\frac{4000}{10}=640+400=1040$

at $C$

$z=\frac{2\left(2000\right)}{25}+\frac{10,000}{10}=160+1000=1160$

$\to z=-1160$ (max value)

He must invest $Rs2000$ in Bond $A,10,000$ in Bond $B$