MHT CET · Maths · Area Under Curves
The maximum value of \(\mathrm{Z}=x+y\), subjected to \(x+y \leq 10,5 x+3 y \geq 15, x \leq 6, x, y \geq 0\)
- A occurs only at unique point
- B occurs only at two distinct points
- C occurs at infinitely many points
- D does not exist
Answer & Solution
Correct Answer
(C) occurs at infinitely many points
Step-by-step Solution
Detailed explanation
Feasible region lies on the origin side of \(x+y=10, x=6\) and non-origin side of \(5 x+3 y=15\)
The corner points of feasible region are \(\mathrm{A}(0,5)\) and \(\mathrm{B}(0,10), \mathrm{C}(6,4), \mathrm{D}(6,0), \mathrm{E}(3,0)\)
At \(\mathrm{A}(0,5), \mathrm{z}=0+5=5\)
At B( 0,10\(), \mathrm{z}=0+10=10\)
At C(6,4), \(z=6+4=10\)
At \(\mathrm{D}(6,0), \mathrm{z}=6+0=6\)
At \(E(3,0), z=3+0=3\)
\(\therefore \mathrm{z}\) has maximum value at \(\mathrm{B}(0,10)\) and \(\mathrm{C}(6,4)\).
\(\therefore \mathrm{z}\) has infinite solution on seg BC .
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