"The maximum or the minimum of the objective function occurs only at the corner points of the feasible region". This theorem is known as fundamental theorem of

The shaded region is the solution set of the inequalities 

The maximum value of $z=6x+8y$ subject to $x-y\ge 0, x+3y\le 12, x\ge 0, y\ge 0$ is

The feasible region of an $\mathrm{LPP}$ is shown in the figure. If $z=3x+9y$, then the minimum value of $z$ occurs at 

Solve graphically the following linear programming problem:

Maximize or minimize $Z=x+2y$ subject to constraints $x+2y\ge 100, 2x-y\le 0, 2x+y\le 200 \& x\ge 0, y\ge 0$.

A furniture trader deals in only two items - chairs and tables. He has $50,000$ rupees to invest and a space to store at most $35$ items. A chair costs him $1000$ rupees and a table costs him $2000$ rupees . The trader earns a profit of $150$ rupees and $250$ rupees on a chair and table, respectively. Formulate the above problem as an LPP to maximise the profit and solve it graphically.