Please help me! My friend has $304 to spend on a fence for her rectangular garden.

Question

she wants to use cedar fencing which cost $15 per meter on one side and cheaper metal fencing which cost four dollars a meter for other three sides. What are the dimensions of the garden in the largest areas you can enclose? Width for other side… Length for cedar side…

Answer 1

15L + 4L + 4(2W) = 304

19L + 8W = 304

8W = 304 -19L

W = 38 -19L/8

Area = LW

A = L(38-19L/8) = 38L - 19L^2/8

A' = 38 -19L/4 = 0

L = (4/19)38 = 8 meters for the cedar on one side

W = 38-(19/8)(8) = 19 meters for the metal fence, on two sides

and another 8 meters of metal on the 3rd side

for total metal fences of 19x2 + 8 = 38+8 = 46 meters of metal

46x4 + 15x8 = 184 + 120 = $304

maximum area = 8x19 = 152 square meters