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

The shaded area in the figure below is the solution set for a certain linear programming problem. Then the linear constraints are given by:

The maximum value of $Z = 10x + 25y$ subject to $0 \leq x \leq 3$,$0 \leq y \leq 3$,and $x + y \leq 5$ occurs at the point:

The Linear Programming Problem ($L$.$P$.$P$.) to minimize $z = 30x + 20y$ subject to the constraints $x + y \leqslant 8$,$x + 2y \geqslant 4$,$6x + 4y \geqslant 12$,$x \geqslant 0$,and $y \geqslant 0$ has:

$A$ dietician has to develop a special diet using two foods $X$ and $Y$. Each packet (containing $30 \ g$) of food $X$ contains $12$ units of calcium,$4$ units of iron,$6$ units of cholesterol and $6$ units of vitamin $A$. Each packet of the same quantity of food $Y$ contains $3$ units of calcium,$20$ units of iron,$4$ units of cholesterol and $3$ units of vitamin $A$. The diet requires at least $240$ units of calcium,at least $460$ units of iron and at most $300$ units of cholesterol. The corner points of the feasible region are:

For the $LPP$,maximize $z=x+4y$ subject to the constraints $x+2y \leq 2$,$x+2y \geq 8$,$x, y \geq 0$.