A Rectangular Parking Lot with a Perimeter of 442 Feet $8050 \mathrm { ft } \leq L \leq 442 \mathrm { ft }$

A rectangular parking lot with a perimeter of 442 feet is to have an area of at least 8050 square feet.Within what bounds must the length of the rectangle lie?

A) $8050 \mathrm { ft } \leq L \leq 442 \mathrm { ft }$
B) $177 \mathrm { ft } \leq L \leq 48 \mathrm { ft }$
C) $49 \mathrm { ft } \leq L \leq 178 \mathrm { ft }$
D) $8050 \mathrm { ft } \leq L \leq 47 \mathrm { ft }$
E) $46 \mathrm { ft } \leq L \leq 175 \mathrm { ft }$