Linear Programm...

Solve the following L.P.P. by graphical method:

Minimize: \(Z=6 x+2 y\) subject to \(x+2 y \geq 3, x+4 y \geq 4,3 x+y \geq 3, x \geq 0, y \geq 0\).

An aeroplane can carry a maximum of 200 passengers. A profit of ₹ 1000 is made on each executive class ticket and a profit of ₹ 600 is made on each economy class ticket. The airline reserves at least 20 seats for executive class. However, at least 4 times as many passengers prefer to travel by economy class than by the executive class. Determine how many tickets of each type must be sold in order to maximise the profit for the airline. What is the maximum profit?

Maximize \(Z=4 x+9 y\), subject to the constraints \(x =0\), y \(=0, x+5 y \leq 200,2 x+3 y \leq 134\).

The problem of maximizing \(z=x_{1}-x_{2}\) subject to constraints \(x_{1}~+~x_{2} \leq 10, ~x_{1} \geq 0, ~x_{2} \geq\) 0 and \(~x_{2} \leq 5\) has:

The minimum of the objective function \(\mathrm{Z}=2 x+10 y\) for linear constraints \(x-y \geq 0, x-5 y \leq-5, x \geq 0\) \(y \geq 0\), is:

Solve the following problem graphically:

Maximise \(Z =3 x+9 y\)

Subject to the constraints:

\(x+3 y \leq 60 \)

\(x+y \geq 10\)

\(x \leq y \)

\(x \geq 0, y \geq 0\)

Solve the linear programming problem by graphical method.

Maximize \(\mathrm{Z}=6 \mathrm{x}+3 \mathrm{y}\), subject to the constraints, \(4 x+y \geq 80, x+5 y \geq 115,3 x+2 y \leq 150, x, y \geq 0\).

Maximize: \(\mathrm{z}=3 \mathrm{x}+5 \mathrm{y}\)

Subject to: \(\mathrm{x}+4 \mathrm{y} \leq 24\)

\(3 \mathrm{x}+\mathrm{y} \leq 21 \)

\(\mathrm{x}+\mathrm{y} \leq 9 \)

\(\mathrm{x} \geq 0, \mathrm{y} \geq 0\)

Consider the Linear Programming function \(z= -3x+4y \) subjected to constraints,\(x+2 y \leq 8,~3 x+2 y \leq 12,~ x \geq 0, ~y \geq 0\), find the minimum value of \(z\).

Region represented by the in equation system \(x+y \leq 3, y \leq 6\) and \(x \geq 0, y \geq 0\) is: