Maximum value of $Z=100 x+70 y$ subject to $2 x \geq 4, y \leq 3, x+y \leq 8, x, y \geq 0$ is

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

The minimum value for the $LPP$ $Z = 6x + 2y$,subject to $2x + y \geq 16$,$x \geq 6$,$y \geq 1$ is

$A$ diet is to contain at least $80$ units of vitamin $A$ and $100$ units of minerals. Two foods $F_{1}$ and $F_{2}$ are available. Food $F_{1}$ costs $Rs. 4$ per unit and food $F_{2}$ costs $Rs. 6$ per unit. One unit of food $F_{1}$ contains $3$ units of vitamin $A$ and $4$ units of minerals. One unit of food $F_{2}$ contains $6$ units of vitamin $A$ and $3$ units of minerals. Formulate this as a linear programming problem. Find the minimum cost for a diet that consists of a mixture of these two foods and also meets the minimal nutritional requirements.

The objective function $z = 4x + 5y$ subject to the constraints $2x + y \geq 7$,$2x + 3y \leq 15$,$y \leq 3$,$x \geq 0$,and $y \geq 0$ has a minimum value at which point?

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: