question_answer

A vertex of the linear inequalities \[2x+3y\le 6\], \[x+4y\le 4\] and \[x,\ y\ge 0\], is 

A)                 (1, 0)     

B)                 (1, 1)

C)                 \[\left( \frac{12}{5},\ \frac{2}{5} \right)\]             

D)                 \[\left( \frac{2}{5},\ \frac{12}{5} \right)\]

Correct Answer: C

Solution :

                Solving \[2x+3y=6\]and \[x+4y=4\], we get \[x=\frac{12}{5},y=\frac{2}{5}\].                 Hence a vertex is \[\left( \frac{12}{5},\frac{2}{5} \right)\].