The maximum value of $z = 3x + 5y$ subject to the constraints $3x + 2y \leq 18$,$x \leq 4$,$y \leq 6$,$x, y \geq 0$,is

In $L.P.P.$,the maximum value of the objective function $Z = 6x + 3y$ subject to the constraints $x + y \leq 5$,$x + 2y \geq 4$,$4x + y \leq 12$,$x, y \geq 0$ is:

The difference between the maximum value and minimum value of the objective function $z = 3x + 5y$ subject to the constraints $x + 3y \leqslant 60$,$x + y \geqslant 10$,$x - y = 0$,and $x, y \geqslant 0$ is:

If the feasible region is as shown in the figure,then the related inequalities are:

In order to supplement daily diet,a person wishes to take some $X$ and some $Y$ tablets. The contents of iron,calcium and vitamins in $X$ and $Y$ (in milligrams per tablet) are given as below:

Tablets	Iron	Calcium	Vitamin
$X$	$6$	$3$	$2$
$Y$	$2$	$3$	$4$

The person needs at least $18$ milligrams of iron,$21$ milligrams of calcium and $16$ milligrams of vitamins. The price of each tablet of $X$ and $Y$ is $Rs. 2$ and $Rs. 1$ respectively. How many tablets of each should the person take in order to satisfy the above requirement at the minimum cost?

$A$ 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 $Rs.\,5000$.