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. The linear constraints are given by:

$A$ wholesale dealer wants to start a business with $Rs. 2,40,000$. The cost price of a quintal of wheat is $Rs. 2000$ and the cost price of a quintal of rice is $Rs. 3000$. He has space capacity for $200$ quintals of grain. The profit from the sale of one quintal of wheat is $Rs. 125$ and that from one quintal of rice is $Rs. 200$. If he has $x$ quintals of rice and $y$ quintals of wheat,then the objective function for the maximum profit is $....$

Cake-$A$ requires $200\, g$ of flour and $25\, g$ of fat. Cake-$B$ 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. The mathematical form of this $LPP$ is $.....$

The maximum value of the objective function $Z = 3x + 2y$ for the linear constraints $x + y \leq 7$,$2x + 3y \leq 16$,$x \geq 0$,$y \geq 0$ is

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