Question:
Which of the following is/are solution of the LPP?
\[
\text{Min }Z=12x+9y
\]
Subject to
\[
x+2y\leq 40,\quad 3x+y\geq 30,\quad 4x+3y\geq 60,\quad x,y\geq 0
\]
A. \((15,0)\),
B. \((40,0)\),
C. \((4,18)\),
D. \((6,12)\),
E. \((10.5,6)\).
Which of the following is/are solution of the LPP?
\[
\text{Min }Z=12x+9y
\]
Subject to
\[
x+2y\leq 40,\quad 3x+y\geq 30,\quad 4x+3y\geq 60,\quad x,y\geq 0
\]
A. \((15,0)\),
B. \((40,0)\),
C. \((4,18)\),
D. \((6,12)\),
E. \((10.5,6)\).
B. \((40,0)\),
C. \((4,18)\),
D. \((6,12)\),
E. \((10.5,6)\).
Show Hint
For LPP optimum questions, substitute each given point in the objective function and compare the values.
Updated On: Jun 6, 2026
- A only
- A and D only
- A, D and E only
- B and C only
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The Correct Option is C
Solution and Explanation
Concept:
In a Linear Programming Problem, the optimum value is checked at feasible corner points. Here, we calculate \(Z=12x+9y\) at the given feasible points.
Step 1: Calculate \(Z\) at point A \((15,0)\). \[ Z=12(15)+9(0)=180 \]
Step 2: Calculate \(Z\) at point B \((40,0)\). \[ Z=12(40)+9(0)=480 \]
Step 3: Calculate \(Z\) at point C \((4,18)\). \[ Z=12(4)+9(18) \] \[ Z=48+162=210 \]
Step 4: Calculate \(Z\) at point D \((6,12)\). \[ Z=12(6)+9(12) \] \[ Z=72+108=180 \]
Step 5: Calculate \(Z\) at point E \((10.5,6)\). \[ Z=12(10.5)+9(6) \] \[ Z=126+54=180 \]
Step 6: Compare values.
Minimum value is: \[ Z_{\min}=180 \] This occurs at: \[ A,\ D,\ E \] \[ \therefore \text{Correct Answer is (C)} \]
In a Linear Programming Problem, the optimum value is checked at feasible corner points. Here, we calculate \(Z=12x+9y\) at the given feasible points.
Step 1: Calculate \(Z\) at point A \((15,0)\). \[ Z=12(15)+9(0)=180 \]
Step 2: Calculate \(Z\) at point B \((40,0)\). \[ Z=12(40)+9(0)=480 \]
Step 3: Calculate \(Z\) at point C \((4,18)\). \[ Z=12(4)+9(18) \] \[ Z=48+162=210 \]
Step 4: Calculate \(Z\) at point D \((6,12)\). \[ Z=12(6)+9(12) \] \[ Z=72+108=180 \]
Step 5: Calculate \(Z\) at point E \((10.5,6)\). \[ Z=12(10.5)+9(6) \] \[ Z=126+54=180 \]
Step 6: Compare values.
Minimum value is: \[ Z_{\min}=180 \] This occurs at: \[ A,\ D,\ E \] \[ \therefore \text{Correct Answer is (C)} \]
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