英文函数题

来源：百度知道 编辑：UC知道 时间：2024/05/06 18:47:35
A rectangular garden next to a building is to be fenced on three sides. Fencing for the side parallel to the building costs $60 per foot, and material for the other two sides costs $40 per foot. If $1,600 is to be spent on fencing, what are the dimensions of the garden with the largest possible area?
parallel side=?
other sides=?

first set parallel side=x and other sides=y

60x+40*2y=1600 (1)

objective function is max(xy)

from (1), we have

3x+4y=80

3x+4y≥2√(3x*4y), and the equal sign is valid when 3x=4y

since x,y>0 so when 3x=4y=40 i.e. x=40/3,y=10, we have the max value of xy, which is the largest area 40/3*10=400/3