List of top Mathematics Questions on Linear Programming

If the system of linear equations
x + y + z = 2, 2x + y − z = 3, 3x + 2y + kz = 4
has a unique solution, then:

Minimize $Z = -50x + 20y$ subject to the constraints: \[ 2x - y \geq -5, \quad 3x + y \geq 3, \quad 2x - 3y \leq 12, \quad x \geq 0, \quad y \geq 0. \] Then which of the following is/are true:
(A) Feasible region is unbounded.
(B) $Z$ has no minimum value.
(C) The minimum value of $Z$ is 100.
(D) The minimum value of $Z$ is -300.

Optimize $Z = 3x + 9y$ subject to the constraints: \[ x + 3y \leq 60, \quad x + y \geq 10, \quad x \leq y, \quad x \geq 0, \quad y \geq 0. \]

The corner points of the feasible region for an L.P.P. are (0, 10), (5, 5), (5, 15), and (0, 30). If the objective function is Z = αx + βy, α, β > 0, the condition on α and β so that maximum of Z occurs at corner points (5, 5) and (0, 20) is:

A person wants to invest 75,000 in options A and B, which yield returns of 8% and 9% respectively. He plans to invest at least 15,000 in Plan A, 25,000 in Plan B, and keep Plan A ≤ Plan B. Formulate the LPP to maximize the return.

Let the two variables $ x $ and $ y $ satisfy the following conditions: \[ x + y \leq 50, \quad x + 2y \leq 80, \quad 2x + y \geq 20, \quad x, y \geq 0. \] Then the maximum value of $ Z = 4x + 3y $ is:

Solve the following L.P.P. by graphical method:
Maximize:
\[ z = 10x + 25y. \] Subject to: \[ 0 \leq x \leq 3, \quad 0 \leq y \leq 3, \quad x + y \leq 5. \]

Minimize Z = 5x + 3y \text{ subject to the constraints} \[ 4x + y \geq 80, \quad x + 5y \geq 115, \quad 3x + 2y \leq 150, \quad x \geq 0, \quad y \geq 0. \]

Maximize $ z = 8000x + 12000y $ subject to constraints: \[ 3x + 4y \leq 60, \quad x + y \leq 30, \quad x \geq 0, \quad y \geq 0. \]

Find the minimum value of \[ Z = 50x + 70y \] $\text{under the following constraints by graphical method:}$ \[ 2x + y \geq 8, \] \[ x + 2y \geq 10, x \geq 0, y \geq 0. \]

Find the maximum value of $ Z = 3x + 4y $ under the constraints \[ x + y \leq 4, x \geq 0, y \geq 0. \]

Find the maximization of $ z = x + y $, under the following constraints: \[ x - y \leq -1, -x + y \leq 0, x \geq 0, y \geq 0. \]

By graphical method solve the LPP under the following constraints: \[ x + 2y \geq 10, \] \[ 3x + 4y \leq 24, \] \[ x \geq 0, \, y \geq 0, \] then find the minimum value of $ z = 200x + 500y $.

Minimize $Z = 6x + 3y$ under the constraints: \[ 4x + y \geq 80, x + 5y \geq 115, 3x + 2y \leq 150, x \geq 0, \; y \geq 0. \]

Maximize $Z = 8000x + 12000y$ under the constraints: \[ 9x + 12y \leq 180, 3x + 4y \leq 60, x + 3y \leq 30, x \geq 0, \; y \geq 0 \]

Solve the inequality $3x + 4y \leq 12$, $4x + 3y \leq 12$, $x \geq 0$, $y \geq 0$ by graphical method.

The electricity bill of a certain establishment is partly fixed and partly varies as the number of units of electricity consumed. When in a certain month 540 units are consumed, the bill is Rs. 1,800. In another month 620 units are consumed and the bill is Rs. 2,040. In yet another month 500 units are consumed. The bill for that month would be

A part of monthly expenses of a family is constant and the remaining varies with the price of wheat. When the rate of wheat is Rs 250 a quintal, the total monthly expenses of the family are Rs 1000 and when it is Rs 240 a quintal, the total monthly expenses are Rs 980. Find the total monthly expenses of the family when the cost of wheat is Rs 350 a quintal.

Pintoo dealt some cards to Minto and himself from a full pack of playing cards and laid the rest aside. Pintoo then said to Mintoo, "If you give me a certain number of your cards I will have 4 times as many cards as you have. If I give you the same number of cards, I will have thrice as many cards as you have." How many cards did Pintoo have?

The monthly incomes of two persons are in the ratio of 4:5 and their monthly expenditures are in the ratio of 7:9. If each saves Rs. 50 a month, then what are their monthly incomes?