Question

A retired person wants to invest an amount of Rs. $50,000.$ His broker recommends investing in two type 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 maximize his returns.

• A. $4900$
• B. $2900$
• C. $5400$
• D. $4000$

Answer 1

The correct option is A $4900$

$Points$	$Z=\frac{10}{100}x+\frac{9}{100}y$
$A(20000,10000)$	$Z=Rs.2900$
$B(40000,10000)$	$Rs.4900$ (Maximize)
$C(25000,25000)$	$Rs.4750$
$D(20000,20000)$	$Rs.3800$

Let $Rs.x$ invest in bond A and $Rs.y$ invest in bond B.

Then A.T.P.

Maximise, $z=\frac{10}{100}x+\frac{9}{100}y$ --- (1)

Subject to constraints

$x+y\le 50,000$ --- (a)

$x\ge 20,000$---(b)

$y\ge 10,000$--- (c)

and $x\ge y$

or $x-y\ge 0$--- (d)

and $x\ge 0,y\ge 0$

Now change inequality into equations

$x+y=50,000,x=20,000,y=10,000,x=y$

Region: put (0, 0) in (a), (b), (c), (d)

$0\le 50000$ (towards origin)

$0\ge 20,000$ (away from origin)

$0\ge 10,000$ (away from origin)

As shown in the graph.

So from the tabular column, we conclude that he has to invest $Rs.40,000$ in 'A' and $Rs.10,000$ in bond 'B' to get maximum return $Rs.4,900.$