Explanation:
(C) : Given,
\(z=50 x+15 y\)
Now, the feasible region is the shaded region. The corner points of the feasible region are \(\mathrm{O}(0,0), \mathrm{A}(20\), \(0), \mathrm{B}(10,50)\) and \(\mathrm{D}(0,60)\).
To find value of \(z=50 x+15 y\) at corner points.
at, \(\quad \mathrm{O}(0,0), \mathrm{z}=0\)
at, \(\quad \mathrm{A}(20,0), \mathrm{z}=50 \times 20+0=1000\)
at, \(\quad \mathrm{B}(10,50), \mathrm{z}=50 \times 10+15 \times 50=1250\)
at, \(\quad \mathrm{D}(0,60), \mathrm{z}=0+15 \times 60=900\)
Thus, maximum value of \(\mathrm{z}=1250\) at \((10,50)\)
i.e. \(\quad x=10\) and \(y=50\)
Hence, the maximum value is 1250 .