KCET · Maths · Linear Programming
For the LPP, maximize \( z=x+4 y \) subject to the constraints \( x+2 y \leq 2, x+2 y \geq 8, x, y \geq 0 \)
- A \( Z_{\max }=4 \)
- B \( Z_{\max }=8 \)
- C \( O_{\max }=16 \)
- D Has no feasible solution
Answer & Solution
Correct Answer
(D) Has no feasible solution
Step-by-step Solution
Detailed explanation
Given equation, \(z=x+4 y\) and constraints, \(x+2 y \leq 2 \rightarrow(1)\) \(\begin{aligned} &\Rightarrow \frac{x}{2}+\frac{y}{2}=1 \\ &x+2 y \geq 8 \rightarrow(2) \\ &\Rightarrow \frac{x}{8}+\frac{y}{4}=1 \\ &x, y \geq 0 \rightarrow(3) \end{aligned}\)
Putting \((0,0)\) in Eq. (1), we get \(0 \leq 2\) which is True. Putting \((0,0)\) in Eq. (2), we get \(0 \geq 8\) which is False. Equation (3) implies that the solution is in first quadrant. From the graph, it has no feasible solution.
Putting \((0,0)\) in Eq. (1), we get \(0 \leq 2\) which is True. Putting \((0,0)\) in Eq. (2), we get \(0 \geq 8\) which is False. Equation (3) implies that the solution is in first quadrant. From the graph, it has no feasible solution.See the Complete Solution
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