Question 1:
The corner points of the feasible region in graphical representation of a L.P.P. are \((2, 72)\), \((15, 20)\) and \((40, 15)\). If \(Z = 18x + 9y\) be the objective function, then
Question 2:
If the feasible region of a linear programming problem with objective function \(Z = ax + by\), is bounded, then which of the following is correct?
Question 3:
A factory produces two products X and Y. The profit earned by selling X and Y is represented by the objective function \(Z=5x+7y,\) where x and y are the number of units of X and Y respectively sold. Which of the following statement is correct?
Question 4:
The corner points of the feasible region of a Linear Programming Problem are (0, 2), (3, 0), (6, 0), (6, 8) and (0, 5). If \(Z=ax+by;\) (a, \(b>0)\) be the objective function, and maximum value of Z is obtained at (0, 2) and (3, 0), then the relation between a and b is:
Question 5:
For a Linear Programming Problem (LPP), the given objective function \(Z=3x+2y\) is subject to constraints: \(x+2y\le10\), \(3x+y\le15\), \(x, y\ge0\). The correct feasible region is:
Question 6:
For a Linear Programming Problem (LPP), the given objective function is \(Z=x+2y\). The feasible region PQRS determined by the set of constraints is shown as a shaded region in the graph. \(P\equiv(\frac{3}{13},\frac{24}{13})\) \(Q\equiv(\frac{3}{2},\frac{15}{4})\) \(R\equiv(\frac{7}{2},\frac{3}{4})\) \(S\equiv(\frac{18}{7},\frac{2}{7})\). Which of the following statements is correct?
Question 7:
In a Linear Programming Problem (LPP), the objective function \(Z=2x+5y\) is to be maximised under the following constraints: \(x+y\le4\), \(3x+3y\ge18\), \(x, y\ge0\). Study the graph and select the correct option. The solution of the given LPP:
Question 8:
A linear programming problem deals with the optimization of a/an:
Question 9:
The number of corner points of the feasible region determined by constraints \(x\ge0, y\ge0, x+y\ge4\) is:
Question 10:
The common region determined by all the constraints of a linear programming problem is called :
Question 11:
The restrictions imposed on decision variables involved in an objective function of a linear programming problem are called :
Question 12:
Of the following, which group of constraints represents the feasible region given below ?
Question 13:
Assertion (A) : Every point of the feasible region of a Linear Programming Problem is an optimal solution.
Reason (R) : The optimal solution for a Linear Programming Problem exists only at one or more corner point(s) of the feasible region.
Question 14:
In a Linear Programming Problem, the objective function \(Z=5x+4y\) needs to be maximised under constraints \(3x+y\le6\), \(x\le1\), \(x, y\ge0\). Express the LPP on the graph and shade the feasible region and mark the corner points.
Question 15:
Solve the following linear programming problem graphically: \[ \text{Maximise} \quad Z = x + 2y\] Subject to the constraints: \[ \begin{aligned} x - y &\geq 0 \\ x - 2y &\geq -2 \\ x &\geq 0, y \geq 0 \end{aligned} \]
Question 16:
Solve the following linear programming problem graphically:
Minimise \(Z=x-5y\)
subject to the constraints:
\(x-y \ge 0\),
\(-x+2y \ge 2\),
\(x \ge 3\),
\(y \le 4\),
\(y \ge 0\)
Question 17:
Solve the following Linear Programming Problem using graphical method: Maximise \(Z=100x+50y\) subject to the constraints \(3x+y\le600\), \(x+y\le300\), \(y\le x+200\), \(x\ge0\), \(y\ge0\).
Question 18:
In the Linear Programming Problem (LPP), find the point/points giving maximum value for \(Z=5x+10y\) subject to constraints \(x+2y\le120\), \(x+y\ge60\), \(x-2y\ge0\), \(x, y\ge0\).
Question 19:
Consider the Linear Programming Problem, where the objective function \(Z=(x+4y)\) needs to be minimized subject to constraints \(2x+y\ge1000\), \(x+2y\ge800\), \(x,y\ge0\). Draw a neat graph of the feasible region and find the minimum value of Z.
Question 20:
In the Linear Programming Problem for objective function \(Z=18x+10y\) subject to constraints \(4x+y\ge20\), \(2x+3y\ge30\), \(x,y\ge0\) find the minimum value of Z.
Question 21:
Solve the following linear programming problem graphically: Maximise \(Z=2x+3y\) subject to the constraints: \(x+y\le6\), \(x\ge2\), \(y\le3\), \(x,y\ge0\).
Question 22:
Solve the following linear programming problem graphically: Maximise \(z=4x+3y.\) subject to the constraints \(x+y\le800\), \(2x+y\le1000\), \(x\le400\), \(x,y\ge0\).
Question 23:
Solve the following linear programming problem graphically: Maximise \(Z=500x+300y\), subject to constraints \(x+2y\le12\), \(2x+y\le12\), \(4x+5y\ge20\), \(x\ge0\), \(y\ge0\).
Question 24:
Solve the following L.P.P. graphically: Maximise \(Z=60x+40y\) Subject to \(x+2y\le12\), \(2x+y\le12\), \(4x+5y\ge20\), \(x,y\ge0\).