Question

A merchant plans to sell two types of personal computers - a desktop model and a portable model that will cost $Rs.25000$ and $Rs.40000$ respectively. He estimates that the total monthly demand of computers will not exceed $250$ units. Determine the number of units of each type of computers which the merchant should stock to get maximum profit if he does not want to invest more than $Rs.70$ lakhs and if his profit on the desktop model is $Rs.4500$ and on portable model is $Rs.5000$.

Answer 1

Let number of desktop model be $x$ and number of portable model be $y$

According to question,

Since, monthly demand doesn't exceed 250 units.

$\therefore x+y\le 250...\left(1\right)$

Since, maximum invest is 70 lakhs.

$\therefore 25000x+40000y\le 7000000\Rightarrow 5x+8y\le 1400...\left(2\right)$

Also, quantity can't be negative.

$\therefore x\ge 0,y\ge 0...\left(3\right)$

We have to maximize profit $Z$

where $Z=4500x+5000y$

After plotting all the constraints given by equation (1),(2) and (3), we got the feasible region as shown in the image.

Corner points	Value of $Z=4500x+5000y$
A(0,175)	875000
B(200,50)	1150000 (Maximum)
C(250,0)	112500

Hence, maximum profit that can be earned by the merchant will be $1150000Rs$