A man rides his motorcycle at the speed of 50km/hour.He has to speed Rs 2 per km on petrol.If he rides it at at a faster speed of 80km/hour,the petrol cost increases to Rs 3 per km.He has at most Rs120 to spend on petrol and one hour's time.He wishes to find the maximum distance that he can travel.Express this problem as a linear programming problem.

Question

$\begin{array}{1 1}(A)\;Z=x+y\; subjected \;to \;constraints 8x+5y\leq 120,2x+3y\leq 120 \\ (B)\;Z=x+y\; subjected \;to \;constraints \;5x+8y\leq 400,2x+3y\leq 120 \\(C)\;Z=x+y\; subjected\; to \;constraints 8x+5y\leq 400,2x+3y\leq 120 \\ (D)Z=x+y\; subjected \;to\; constraints \;8x+5y\leq 100,2x+3y\leq 120\end{array}$