MHT CET · Maths · Linear Programming
The minimum value of \(\mathrm{Z}=5 x+8 y\) subject to \(x+y \geq 5,0 \leq x \leq 4, y \geq 2, x \geq 0\) \(y \geq 0\) is
- A 40
- B 36
- C 31
- D 20
Answer & Solution
Correct Answer
(C) 31
Step-by-step Solution
Detailed explanation
(C)
Required area is shaded.
Co-ordinates of vertices are \(C \equiv(4,1)\);
\(D \equiv(4,2)\) and \(P \equiv(3,2)\)
\(\mathrm{Z}=5 \mathrm{x}+8 \mathrm{y}\)
\(\therefore \quad Z_{(C)}=20+8=28\)
\(\mathrm{Z}_{(\mathrm{D})}=20+16=36\)
\(Z_{(P)}=15+16=31\)
Minimum value will be 28 .
Required area is shaded.
Co-ordinates of vertices are \(C \equiv(4,1)\);
\(D \equiv(4,2)\) and \(P \equiv(3,2)\)
\(\mathrm{Z}=5 \mathrm{x}+8 \mathrm{y}\)
\(\therefore \quad Z_{(C)}=20+8=28\)
\(\mathrm{Z}_{(\mathrm{D})}=20+16=36\)
\(Z_{(P)}=15+16=31\)
Minimum value will be 28 .
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