Question

A merchant plans to sell two products $A$ and $B$ costs $\text{Rs}25000$ and $\text{Rs}40000$ respectively. He estimates that the total monthly demand of products will not exceed $250$ units. If he does not want to invest more than $\text{Rs}70$ lakhs and if his profits on product $A$ is $\text{Rs}4500$ and on $B$ is $\text{Rs}5000.$ Then number of products $A$ stocked to get maximum profit is

Answer 1

Let $x,y$ number of product $A$ and $B$ is stocked.
Objective function : $Z=4500x+5000y$
Constraints :
maximum units stored is $250,$
$\Rightarrow x+y\le 250\cdots \left(i\right)$
maximum investment is $\text{Rs}70$ lakhs
$\Rightarrow 25000x+40000y\le 7000000\Rightarrow 5x+8y\le 1400\cdots \left(ii\right)$
and $x,y\ge 0\cdots \left(iii\right)$
Plotting the graph of given constraints :
We get, our feasible region as $OBEC,$
now tabulating the value of objective function $Z=4500x+5000y$ at corner points :

Corner points : $(x,y)$	Value : $Z=4500x+5000y$
$O(0,0)$	$0$
$B(0,175)$	$875000$
$E(200,50)$	$1150000$
$C(250,0)$	$1125000$

we can see that maximum profit he gets by stocking $200$ units of product $A$ and $50$ units of product $B$