Answer:
Dimensions that minimize is; 20 ft x 100 ft
Step-by-step explanation:
Let the width and length be x and y respectively.
We are given area as 2000 Sq.ft.
Thus;
xy = 2000 - - - (eq 1)
We are told that the brick wall costs $20 per linear foot and the chain link costs $4 per linear foot. Thus;
C(x) = 20x + 4y
From eq(1),y = 2000/x
Thus;
C(x) = 20x + 4(2000/x)
C(x) = 20x + 8000/x
To minimize this, we will differentiate and equate to 0.
Thus;
C'(x) = 20 - 8000/x²
Equating to zeeo;
20 - 8000/x² = 0
20 = 8000/x²
20x² = 8000
Divide both sides by 20;
x² = 8000/20
x² = 400
x = √400
x = 20 ft
Putting 20 for x in eq 1,we have;
20y = 2000
y = 2000/20
y = 100 ft
