Question:
Consider the Linear Programming Problem (LPP): Maximize $z = 30x + 60y$ subject to constraints $x + 2y \leq 12$, $2x + y \leq 12$, $4x + 5y \geq 20$, $x \geq 0$, $y \geq 0$. Then the number of corner points of the feasible region is
Consider the Linear Programming Problem (LPP): Maximize $z = 30x + 60y$ subject to constraints $x + 2y \leq 12$, $2x + y \leq 12$, $4x + 5y \geq 20$, $x \geq 0$, $y \geq 0$. Then the number of corner points of the feasible region is
Show Hint
Always consider only feasible intersections (satisfying all inequalities).
Updated On: Apr 24, 2026
- $8$
- $6$
- $3$
- $4$
- $5$
Show Solution
Verified By Collegedunia
The Correct Option is
Solution and Explanation
Concept:
• Corner points are intersections of constraint lines
Step 1: Plot constraints
\[ x + 2y = 12,\quad 2x + y = 12,\quad 4x + 5y = 20 \]
Step 2: Consider region
Region lies in first quadrant satisfying all inequalities.
Step 3: Find intersections
Each pair of lines intersects giving vertices.
Step 4: Count feasible vertices
After checking all constraints, total corner points = 5 Final Conclusion:
\[ = 5 \]
• Corner points are intersections of constraint lines
Step 1: Plot constraints
\[ x + 2y = 12,\quad 2x + y = 12,\quad 4x + 5y = 20 \]
Step 2: Consider region
Region lies in first quadrant satisfying all inequalities.
Step 3: Find intersections
Each pair of lines intersects giving vertices.
Step 4: Count feasible vertices
After checking all constraints, total corner points = 5 Final Conclusion:
\[ = 5 \]
Was this answer helpful?
0
0
Top KEAM Mathematics Questions
- If $\int e^{2x}f' \left(x\right)dx =g \left(x\right)$, then $ \int\left(e^{2x}f\left(x\right) + e^{2x} f' \left(x\right)\right)dx =$
- The value of $ \cos [{{\tan }^{-1}}\{\sin ({{\cot }^{-1}}x)\}] $ is
- The solutions set of inequation $\cos^{-1}x < \,\sin^{-1}x$ is
- Let $\Delta= \begin{vmatrix}1&1&1\\ 1&-1-w^{2}&w^{2}\\ 1&w&w^{4}\end{vmatrix}$, where $w \neq 1$ is a complex number such that $w^3 = 1$. Then $\Delta$ equals
- Let $p : 57$ is an odd prime number, $\quad \, q : 4$ is a divisor of $12$ $\quad$ $r : 15$ is the $LCM$ of $3$ and $5$ Be three simple logical statements. Which one of the following is true?
View More Questions
Top KEAM Linear Programming Problem Questions
- In a linear programming problem ,the restrictions under which the objective function is to be optimized are called as?
- The feasible region for a L.P.P. is shown in the figure below. Let z = 50x+15y be the objective function, then the maximum value of z is
- Consider the linear programming problem:
Maximize z=10x+5y
subject to the constraints
2x+3y≤120
2x + y ≤ 60
x,y≥0.
Then the coordinates of the corner points of the feasible region are - The constraints of a linear programming problem are x+2y≤10 and 6x+3y≤18. Which of the following points lie in the feasible region?
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:
View More Questions
Top KEAM Questions
- i.$\quad$ They help in respiration ii.$\quad$ They help in cell wall formation iii.$\quad$ They help in DNA replication iv. $\quad$They increase surface area of plasma membrane Which of the following prokaryotic structures has all the above roles?
- A body oscillates with SHM according to the equation (in SI units), $x = 5 cos \left(2\pi t +\frac{\pi}{4}\right) .$ Its instantaneous displacement at $t = 1$ second is
- The pH of a solution obtained by mixing 60 mL of 0.1 M BaOH solution at 40m of 0.15m HCI solution is
Kepler's second law (law of areas) of planetary motion leads to law of conservation of
- If $\int e^{2x}f' \left(x\right)dx =g \left(x\right)$, then $ \int\left(e^{2x}f\left(x\right) + e^{2x} f' \left(x\right)\right)dx =$
View More Questions