Question:
Minimize Z = 5x + 3y \text{ subject to the constraints} \[ 4x + y \geq 80, \quad x + 5y \geq 115, \quad 3x + 2y \leq 150, \quad x \geq 0, \quad y \geq 0. \]
Minimize Z = 5x + 3y \text{ subject to the constraints} \[ 4x + y \geq 80, \quad x + 5y \geq 115, \quad 3x + 2y \leq 150, \quad x \geq 0, \quad y \geq 0. \]
Show Hint
In linear programming, the optimal solution occurs at one of the corner points of the feasible region.
Updated On: Mar 2, 2025
Hide Solution
Verified By Collegedunia
Solution and Explanation
Step 1: Graph the constraints to form the feasible region.
Step 2: The objective function is \( Z = 5x + 3y \). Find the corner points of the feasible region.
Step 3: Evaluate \( Z \) at each corner point.
Step 4: Choose the corner point that gives the minimum value of \( Z \).
Was this answer helpful?
0
0
Top Questions on Linear Programming
- The feasible region is bounded by the inequalities: \[ 3x + y \geq 90, \quad x + 4y \geq 100, \quad 2x + y \leq 180, \quad x, y \geq 0 \] If the objective function is $ Z = px + qy $ and $ Z $ is maximized at points $ (6, 18) $ and $ (0, 30) $, then the relationship between $ p $ and $ q $ is:
- CUET (UG) - 2025
- Mathematics
- Linear Programming
Solve the following LPP graphically: Maximize: \[ Z = 2x + 3y \] Subject to: \[ \begin{aligned} x + 4y &\leq 8 \quad \text{(1)} \\ 2x + 3y &\leq 12 \quad \text{(2)} \\ 3x + y &\leq 9 \quad \text{(3)} \\ x &\geq 0,\quad y \geq 0 \quad \text{(non-negativity constraints)} \end{aligned} \]
- CBSE CLASS XII - 2025
- CBSE Compartment XII - 2025
- Mathematics
- Linear Programming
- In an LPP, corner points of the feasible region determined by the system of linear constraints are \((1,1), (3,0), (0,3)\). If \(Z = ax + by\), where \(a>0, b>0\) is to be minimized, the condition on \(a\) and \(b\) so that the minimum of \(Z\) occurs at \((3, 0)\) and \((1, 1)\) will be:
- CBSE CLASS XII - 2025
- CBSE Compartment XII - 2025
- Mathematics
- Linear Programming
- The maximum value of \(Z = 3x + 4y\) subject to the constraints \(x + y \leq 1\), \(x \geq 0\), \(y \geq 0\) is:
- CBSE CLASS XII - 2025
- CBSE Compartment XII - 2025
- Mathematics
- Linear Programming
- Corner points of a feasible bounded region are \((0, 10)\), \((4, 2)\), \((3, 7)\) and \((10, 6)\). Maximum value 50 of objective function \(z = ax + by\) occurs at two points \((0, 10)\) and \((10, 6)\). The value of \(a\) and \(b\) are:
- CUET (UG) - 2025
- Mathematics
- Linear Programming
View More Questions
Questions Asked in UP Board XII exam
- If \(A = \begin{bmatrix} 3 & 1 \\ -1 & 2 \end{bmatrix}\), then show that \(A^2 - 5A + 7I = O\). Using this, obtain \(A^{-1}\).
- UP Board XII - 2025
- Matrices
- If \( y = \sin^{-1} x \), then prove that \( (1 - x^2) \frac{d^2y}{dx^2} - x \frac{dy}{dx} = 0 \).
- UP Board XII - 2025
- Differential Equations
- If \(A = \begin{bmatrix} 1 & 3 & 3 \\ 1 & 4 & 3 \\ 1 & 3 & 4 \end{bmatrix}\), then find \(A^{-1}\).
- UP Board XII - 2025
- Matrices
- Solve: \( (1 + x^2)\frac{dy}{dx} + 2xy - 4x^2 = 0 \).
- UP Board XII - 2025
- Differential Equations
- Prove that \(\int_0^\pi \sqrt{\frac{1+\cos 2x}{2}} \, dx = 2\).
- UP Board XII - 2025
- Calculus
View More Questions