Answer:
the numbers are missing, so I looked for a similar question:
A fence must be built to enclose a rectangular area of 20,000 ft². Fencing material costs $2.50 per foot for the two sides facing north and south and $3.20 per foot for the other two sides. Find the cost of the least expensive fence.
we must first write down the area and perimeter equations, where X = sides facing north and south, and Y = sides facing east and west.
area ⇒ XY = 20000
perimeter ⇒ P = 2X + 2Y
X = 20,000 / Y
now we replace X in the second equation:
P = 2 · 20000/Y + 2Y
P = 40000/Y + 2Y
now we write down our cost equation:
cost = C(y) = (2.50 · 40000/Y) + (3.20 · 2Y)
cost = C(y) = 6.4Y + 100000/Y
to determine the minimum cost we must find the derivative of the cost equation:
C'(y) = 6.4 - 100000/Y²
now, C'(y) = 0
0 = 6.4 - 100000/Y²
100000/Y² = 6.4
Y² = 100000/6.4 = 15,625
Y = √15,625 = 125
this means that Y = 125 feet
X = 20000/125 = 160 feet
perimeter = (2 · 160) + (2 · 125) = 320 + 250 = 570 feet
cost of fence = (320 · $2.50) + (250 · $3.20) = $1,600