Introduction to Optimization

We at ask-math believe that educational material should be free for everyone. Please use the content of this website for in-depth understanding of the concepts. Additionally, we have created and posted videos on our youtube.

We also offer One to One / Group Tutoring sessions / Homework help for Mathematics from Grade 4th to 12th for algebra, geometry, trigonometry, pre-calculus, and calculus for US, UK, Europe, South east Asia and UAE students.

Affiliations with Schools & Educational institutions are also welcome.

Please reach out to us on [email protected] / Whatsapp +919998367796 / Skype id: anitagovilkar.abhijit

We will be happy to post videos as per your requirements also. Do write to us.

Introduction to optimization : Optimization is one of the most common applications of calculus involves the determination of minimum and maximum values. In general we hear terms such as greatest profit, least cost, least time, greatest voltage, optimum size, least size, large as possible, maximum and minimum.

For optimization problems, the following results will be very useful.
1) For a square of side 'x', we have,
Area = $x^{2}$ and Perimeter = 4x.

2) For rectangle of sides x and y, we have,
Area = xy and Perimeter = 2(x + y)

3) For trapezoid, we have,
Area = 1/2( a + b)*h where a and b are two opposite parallel sides and h is the height.

4) For circle of radius r, we have,
Area = $\pi r^{2}$ , Circumference = r$\pi$r

5) For sphere of radius r, we have ,
Surface area = 4$\pi r^{2}$ , Volume = 4/3 $\pi r^{3}$

6) For a right circular cylinder of base radius r and height h, we have
Surface area = 2$\pi$ r(r + h), Curved surface area = 2$\pi$ rh, Volume = $\pi r^{2}$ h

7) For right circular cone of height h, slant height 'l' and radius of the base r, we have
Surface area = $\pi$ r (r + l) , Curved surface area = $\pi$ r l , Volume = 1/3 $\pi r^{2}$ h

8) For a rectangular prism of length x , y and z, we have
Surface area = 2(xy + yz + xz) and Volume = xyz

9) For a cube of edge length x, we have
Surface area = 6$x^{2}$ , Volume = $x^{3}$

10) Area of equilateral triangle = $\frac{\sqrt{3}(side)^{2}}{4}$

Remark : It should be noted that if k is a positive constant, then a function of the form kf(x), k + f(x),$[f(x)^{k}]$, $[f(x)^{1/k}]$, logf(x) will be maximum or minimum according as f(x) is maximum or minimum provided that f(x) > 0.

12th grade math

Home

Russia-Ukraine crisis update - 3rd Mar 2022

The UN General assembly voted at an emergency session to demand an immediate halt to Moscow's attack on Ukraine and withdrawal of Russian troops.