Question

5) A wall is to be constructed around the three sides of the rectangle of area480 square
meters, with a fence running along the length of one side. The construction cost for the
wall is Rs190/m, while the cost to build a fence is Rs70/m. Determine the total cost
required for the project.​

Answer 1

the total cost is Rs 13773

Let the length be x and the breadth be y

then, area = xy ⇒ xy = 480 sq m ⇒ y = 480/x m    (1)

To find the least amount of money that must be allotted for the construction of such a fence,

f(x) = 190x + 190x +190y + 70y = 380x + 260y = 380x + (260*480/x)

Now, we equate f'(x) = 0 and find x

f'(x) = 0 ⇒ f'(x) ⇒ 380 = (260*480/x^2) ⇒ x^2 = (260*480)/380 = 328.421       ⇒ x = 18.12 m

therefore, y = 480/x = 480/18.12 = 26.49 m

Cost = Rs (380*18.12 + 260*26.49) = Rs 13773