There are $572 available to build a fence around a rectangular garden. One side must be reinforced and will cost $14 per foot. The other three sides can be built for $8 per foot. Find the dimensions of the largest possible garden which can be built under these constraints.
The reinforced wall will be.................. feet.
The other dimension is ...................feet.
The resulting area is square ................feet
.
thank you
The reinforced wall will be.................. feet.
The other dimension is ...................feet.
The resulting area is square ................feet
.
thank you
-
13
143/8
1859/8 = 232.375 square feet
method:
x = width
$14*x + $8*x + 2*$8*( (572 - 22x)/16 ) = $572
area = x * length = x * (572 - 22x)/16 = (286/8)x - (11/8)xx
derivative of area: (143/4) - (11/4)x
maximized at x = 143/11 = 13
so largest area = 13 X (143/8) = (1859/8) = 232.375 square feet
check:
$14*13 + $8*13 + 2*$8*(143/8) = $572
143/8
1859/8 = 232.375 square feet
method:
x = width
$14*x + $8*x + 2*$8*( (572 - 22x)/16 ) = $572
area = x * length = x * (572 - 22x)/16 = (286/8)x - (11/8)xx
derivative of area: (143/4) - (11/4)x
maximized at x = 143/11 = 13
so largest area = 13 X (143/8) = (1859/8) = 232.375 square feet
check:
$14*13 + $8*13 + 2*$8*(143/8) = $572