question_answer

The corner points of the feasible region determined by the system of linear constraints are\[\left( \mathbf{0},\mathbf{10} \right),\left( \mathbf{5},\mathbf{5} \right),\left( \mathbf{15},\mathbf{15} \right),\left( \mathbf{0},\mathbf{20} \right)\]. Let\[\mathbf{Z}=\mathbf{px}+\mathbf{qy}\], where\[\mathbf{p},\mathbf{q}>\mathbf{0}\]. Condition on p and q so that the maximum of Z occur sat both the points \[\left( \mathbf{15},\mathbf{15} \right)\] and (0, 20) is

A) \[p=q\]            

B) \[p=2q\]        

C) \[q=2p\]                       

D) \[q=3p\]