Linear Programm...

Determine graphically the minimum value of the objective function. \(Z=-50 x+20 y\)

Subject to constraints

\(2 x-y \geq-5 \)

\(3 x+y \geq 3 \)

\(2 x-3 y \leq 12 \)

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

Maximize \(\mathrm{Z}=\mathrm{x}+2 \mathrm{y}\), subject to the constraints

\(\mathrm{x}+2 \mathrm{y} \geq 100 \)

\(2 \mathrm{x}-\mathrm{y} \leq 0 \)

\(2 \mathrm{x}+\mathrm{y} \leq 200\)

\(\mathrm{x}, \mathrm{y} \geq 0\) by graphical method.

Consider a Linear Programming function\(Z=2 x+5 y\) subjected to constraints\(x+4 y \leq 24,~3 x+y \leq 21\) and \(x+\) \(y \leq 9\)where, \(x \geq 0\) and \(y \geq 0\). What will be the maximum value of the Linear programming function?

A manufacturer has three machines I, II and III installed in his factory. Machines I and II are capable of being operated for at most 12 hours whereas machine III must be operated for atleast 5 hours a day. She produces only two items M and N each requiring the use of all the three machines. The number of hours required for producing 1 unit of each of M and N on the three machines are given in the following table:

She makes a profit of Rs 600 and Rs 400 on items M and N respectively. How many of each item should she produce so as to maximise her profit assuming that she can sell all the items that she produced? What will be the maximum profit?

Maximam value of : \(Z=10 x+25y\) Subject to:

\(x \leq 3, y \leq 3, x+y \leq 5, x \geq 0, y \geq 0\) at:

For the following LPP:

\(\text { Max. } Z=-0.1 x_{1}+0.5 x_{2} \)

\(2 x_{1}+5 x_{2} \leq 80 \)

\(x_{1}+x_{2} \leq 20 \)

\(x_{1}, x_{2} \geq 0\)

to get the optimum solution, the values of \(x_{1}, x_{2}\) are:

The feasible region (shaded) for a L.P.P is shown in the figure. The maximum \(\mathrm{Z}=5 \mathrm{x}+\) \(7 y\) is:

How many maximum value is there in the Linear Programming function given by\(z=x+y\), subjected to \(x-y \leq-1, ~-x+y \leq 0,~\text{and}~ x, y \leq 0\) conditions?

Solve the linear programming problem by graphical method:

Minimize \(Z=3 x+2 y\) Subject to the constraints \(x+y \geq 8,3 x+5 y \leq 15\) and \(x \geq 0, y \leq 15\).

Maximize \(Z=3 x+5 y\) Subject to:

\(x+2 y \leq 20 \)

\(x+y \leq 15 \)

\(y \leq 5 \)

\(x, y \geq 0\)