MHT CET · Maths · Linear Programming
For a feasible region \(O C D B O\) given below, the maximum value of the objective function \(z=3 x+4 y\) is
- A 70
- B 100
- C 110
- D 130
Answer & Solution
Correct Answer
(C) 110
Step-by-step Solution
Detailed explanation
Corner points of the given feasible region are \(\mathrm{O}(0,0), \mathrm{C}(10,10), \mathrm{D}(10,20), \mathrm{B}(0,25)\)
\(\therefore \quad \mathrm{z}\) at \(\mathrm{C}(10,10)=70\),
\(\mathrm{z}\) at \(\mathrm{D}(10,20)=110\),
\(\mathrm{z}\) at \(\mathrm{B}(0,25)=100\)
\(\therefore \quad\) The maximum value of \(\mathrm{z}\) is 110 .
\(\therefore \quad \mathrm{z}\) at \(\mathrm{C}(10,10)=70\),
\(\mathrm{z}\) at \(\mathrm{D}(10,20)=110\),
\(\mathrm{z}\) at \(\mathrm{B}(0,25)=100\)
\(\therefore \quad\) The maximum value of \(\mathrm{z}\) is 110 .
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