List of top Mathematics Questions on Linear Programming Problem

Solve the following linear programming problem graphically: \[ \text{Minimise } Z = 2x + y \] subject to the constraints: \[ 3x + y \geq 9, \] \[ x + y \geq 7, \] \[ x + 2y \geq 8, \] \[ x, y \geq 0. \]

The feasible region along with corner points for a linear programming problem are shown in the graph. Write all the constraints for the given linear programming problem.

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.

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 statements is correct?

In a linear programming problem (L.P.P.), the corner points of the feasible region are $ (5, 0), (10, 0) $ and $ (4, 1) $. Find the maximum value of $ Z = 2x + 3y $.

In a linear programming problem (L.P.P.), the corner points of the feasible region are $ (5, 0), (10, 0) $ and } $ (4, 1) $. Find the maximum value of $ Z = 2x + 3y $.

The feasible region of the linear programming problem is determined by the system of inequalities: \[ x + y \leq 6, \quad x \geq 0, \quad y \geq 0. \] What is the maximum value of $ x + y $ in the feasible region?

The maximum value of $ z = 3x + 4y $, subject to the constraints $ x + y \leq 40, x + 2y \geq 60 $ and $ x, y \geq 0 $ is:

Consider the following statements: Statement (I): In a LPP, the objective function is always linear. Statement (II): In a LPP, the linear inequalities on variables are called constraints. Which of the following is correct?

Given the Linear Programming Problem:
Maximize $ z = 11x + 7y $ subject to the constraints: $ x \leq 3 $, $ y \leq 2 $, $ x, y \geq 0 $.
Then the optimal solution of the problem is:

The maximum value of $ P = 500x + 400y $ for the given constraints $ x + y \leq 200, \quad x \geq 20, \quad y \geq 4x, \quad y \geq 0 $

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

The maximum value of $ P = 8x + 3y $, subject to the constraints $ x + y \leq 6, x \geq 0, y \geq 0 $, is

Corner points of the feasible region for an LPP are $(0, 2), (3, 0), (6, 0), (6, 8)$ and $(0, 5)$. Let $z = 4x + 6y$ be the objective function. The minimum value of $z$ occurs at:

Solve the following linear programming problem graphically:
Maximize $ z = x + y $, subject to constraints:
\[ 2x + 5y \leq 100, \quad 8x + 5y \leq 200, \quad x \geq 0, \quad y \geq 0. \]

The restrictions imposed on decision variables involved in an objective function of a linear programming problem are called:

If $ x + y \leq 55 $ and $ x + y \geq 10 $, with $ x \geq 0 $, $ y \geq 0 $, then the minimum value of the objective function $ z = 7x + 3y $ is: \hfill \break

If the vertices of the finite feasible solution region are $ (0, 6), (3, 3), (9, 9), (0, 12) $, then the maximum value of the objective function $ z = 6x + 12y $ is __________.

It is given that function $ f(x) = x^4 - 62x^2 + ax + 9 $ attains a local maximum value at $ x = 1 $. Find the value of $ a $, hence obtain all other points where the given function $ f(x) $ attains local maximum or local minimum values.

A function $ f(x) = |1 - x + |x|| $ is:

Solve the following linear programming problem graphically: \[ {Maximise } z = 4x + 3y, \quad {subject to the constraints:} \] \[ x + y \leq 800, \quad 2x + y \leq 1000, \quad x \leq 400, \quad x, y \geq 0. \]

The restrictions imposed on decision variables involved in an objective function of a linear programming problem are called:

Maximize $ z = x + y $ subject to: \[ x + y \leq 10, \quad 3y - 2x \leq 15, \quad x \leq 6, \quad x, y \geq 0. \] Find the maximum value.

The minimum value of $ Z = 3x + 5y $, given subject to the constraints $ x + y \geq 2 $, $ x + 3y \geq 3 $, $ x, y \geq 0 $, is:

The maximum value of $ Z = 12x + 13y $, subject to constraints $ x \geq 0, \quad y \geq 0, \quad x + y \leq 5, \quad 3x + y \leq 9 $ is