The maximum value of $2x + y$ subject to $3x + 5y \leq 26$ and $5x + 3y \leq 30, x \geq 0, y \geq 0$ is

The correct constraints for the given feasible region are:

The maximum value of $z=7x+8y$ subject to the constraints $x+y \leq 20, y \geq 5, x \leq 10, x \geq 0, y \geq 0$ is

The $L$.$P$.$P$. to maximize $z=x+y$,subject to $x+y \leq 30, x \leq 15, y \leq 20, x+y \geq 15$,and $x, y \geq 0$ has

One kind of cake requires $200 \,g$ of flour and $25 \,g$ of fat,and another kind of cake requires $100 \,g$ of flour and $50 \,g$ of fat. Find the maximum number of cakes which can be made from $5 \,kg$ of flour and $1 \,kg$ of fat,assuming that there is no shortage of the other ingredients used in making the cakes.

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