For the feasible region $OCDBO$ shown in the figure,the maximum value of the objective function $z = 3x + 4y$ is:

The difference between the maximum and minimum values of the objective function $Z = 3x + 5y$, subject to the constraints $x + 3y \leq 60$, $x + y \geq 10$, $x - y \leq 0$, and $x, y \geq 0$, is

The maximum value of $z=3x+4y$,subject to the constraints $x+y \leq 40$,$x+2y \leq 60$ and $x, y \geq 0$ is

The maximum value of $z=50x+15y$ subject to the constraints $x+y \leq 60$,$5x+y \leq 100$,$x \geq 0$,$y \geq 0$ is at the point:

The shaded part of the given figure indicates the feasible region. Then the constraints are

$A$ dietician has to develop a special diet using two foods $P$ and $Q$. Each packet (containing $30 \, g$) of food $P$ 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 $Q$ 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. How many packets of each food should be used to maximize the amount of vitamin $A$ in the diet? What is the maximum amount of vitamin $A$ in the diet?