The $L$.$P$.$P$. to maximize $Z = x + y$,subject to $x + y \leq 1$,$2x + 2y \geq 6$,$x \geq 0$,$y \geq 0$ has

Find the point at which the objective function $Z = x + y$ attains its maximum value subject to the constraints $x + 2y \leq 70$, $2x + y \leq 95$, $x \geq 0$, and $y \geq 0$.

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

Solve the following linear programming problem graphically:
Maximise $Z = 4x + y$......$(1)$
subject to the constraints:
${x + y \leqslant 50}$.......$(2)$
${3x + y \leqslant 90}$......$(3)$
${x \geqslant 0, y \geqslant 0}$......$(4)$

$A$ 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 $....$

The difference between the maximum value and minimum value of the objective function $z = 3x + 5y$ of a linear programming problem subject to constraints $5x + 10y \leq 50$, $x + y \geq 1$, $y \leq 4$, $x \geq 0$, $y \geq 0$ is $3\lambda$. Then the value of $\lambda$ is