MAXIMUM LIGHT ADMITTED FROM A WINDOW

1 INTRODUCTION

”Finding the dimensions of a window of a given perimeter such that it admits maximum light in a room”, is a mathematical problem that can be solved by using differential equation and application of derivative.Sometimes we think that dividing perimeter of a window in equal dimensions, results in maximum admitted light in a room but we also think that may be by taking length more and width less or vice versa we,ll get maximum admitted light.But this is all our hypothication,we can actually calculate the exact dimensions of a window by using differential equations and application of derivative.

2 APPLICATIONS OF THE PROBLEM

1.The real life application of differential equation and application of derivative is that we can arrange the things of given dimensions in a room or at any place in such a way that we’ll get maximum empty area in a room or at any place.

2.Another application is that we can find the dimension of a water tank(i.e height and radius of cylinder) such it takes maximum water.

To summarize, we can conclude that we can find the dimensions of the window so that it admits greatest amount of light.Similarly we can find the dimensions of a box of given material such that it contains maximum things inside it by using the same application with a only difference is that here we have to maximize the volume of the box.