A farmer wants to fence in a rectangular plot in a large field, using a rock wall which is already there as the north boundary. The fencing for the east and west sides of the plot will cost $4 a yard, but the farmer needs to use special fencing which cost $5 a yard on the south side of a plot. If the area of the plot is to be 600 square yards, find the dimensions for the plot which will minimize the cost of the fencing.

Hello,

Let's assume x the length of the north's wall

and y the length of west side .

Area:x*y=600  ==> y=600/x

Cost: 2*y*4+5*x=8y+5x= 4800/x+5x

Minimize cost: (4800/x+5x)'=0

-4800/x²+5=0

x²=4800/5

x²=960

f(x) = - 2/3x + 5; f(5/2)

substitute 5/2 in for x:

f(5/2) = -2/3(5/2) + 5

simplify the right side:

f(5/2) = -5/3 + 5

f(5/2) = 10/3

answer:

f(5/2) = 10/3

i hope this you!

6,250

step-by-step explanation:

to get the area, multiply 360 by 160.(57,600)

to find out how many bags of fertilizer it will take, first figure out how many square feet one bag can hold. divide 1000 by 8(125) to get the unit rate(how many square feet one pound of fertilizer can hold)and multiply it by 50(6250). if i haven't made a mistake, that is the answer.