A) \[14x+5y\ge 70,\,\,\,y\le 14\] and \[x-y\ge 5\]
B) \[14x+5y\le 70,\,\,\,y\le 14\] and \[x-y\ge 5\]
C) \[14x+5y\ge 70,y\ge 14\] and \[x-y\ge 5\]
D) \[14x+5y\ge 70,y\le 14\] and \[x-y\le 5\]
Correct Answer: D
Solution :
[d] From the figure it is clear that there are 3 lines. Line which passes from (0, 14) and (19, 14) is \[y=14\] \[\therefore \] In the shaded region \[0\le y\le 14\] Line which passes from \[(5,0)\] and \[(0,\,\,14)\] is \[14x+5y=70\] \[\therefore \] In the shaded region \[14x+5y\ge 70\] Line which passes form \[(5,0)\] and \[(19,14)\] is \[x-y-5=0\] \[\therefore \] In the shaded region \[x-y\le 5\] Thus, inequations are \[14x+5y\ge 70,\] \[x-y\le 5,\]\[y\le 14.\]
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