Application of Differentiation for Construction Work

This section of mathematics helps us to improve the construction especially when we design a particular building, road, service, etc. In fact, this knowledge will be beneficial when you analyse the most constructive method for a particular work that leads toward a lesser cost while producing the most effective outcome. This form of application can be used not only in the construction field but also in any type of productions.

Now let’s see how this knowledge is applied when designing something cost effective. For an example, If we assume that we need to construct a water supply plant to distribute water for 3 cities, and the 3 cities are A, B & C, when cities are located as follows where distance between AB and AC are exactly the same. We need to identify the most suitable location to construct it which has the shortest lengths of supply lines.

From the geometry of these 3 cities, we can decide the proposed plant should be somewhere inside the triangle and vertically going through city “A” and Midpoint of BC. We will name the location of the plant as “D”.

Now measure the required lengths of supply line regarding the above figure.

Require lengths of supply line (L) = z + 2y

Let’s convert this equation as follows.

To get the shortest length for supply line, it is required dL/dx to be zero.

Hence, the water supply plant (D) should be located on the vertical line from the city "A" by a distance of (16 - x) km.

Therefore, plant should be placed by a distance of 12.54 km from city "A".