Question

1. What is the name of the method we use to find optimal solutions when given a function and at least one constraint?

2. Give a real-life example of an optimization problem in your academic discipline (a function of several variables with constraints).

3. Write a paragraph about the importance of this topic in science, technology, engineering, and mathematics (STEM) research.

Answer 1

1) The name of the problem is linear programming which is a class of optimization problem. The method used to solve this called the simplex method

2) suppose a manufacturer of bottle juice wants to maximize its revenue. he earns $5 by manufacturing juice1 and $8 my manufacturing juice2. he has only capable of making 2000 bottles per day. It takes $1 for making juice1 and &1.5 for juice2. the total budget is $40000. the LPP is given as

supposing he makes x unit of juice1 and y unit of juice2

maximize 5x+8y

subject to constraint:

x+y<= 2000

x+1.5y <= 40000

x>=0 and y>=0

3) optimization is required in every industry. without optimization, an industry cannot compete with its competitor neither it will survive. In engineering, an optimization technique is used to build bridges of having high strength with minimum use of material. In medical science, optimization is required to find a vaccine that has a minimum harmful impact on the host but has maximum impact on parasites. In mathematics, optimization is used to find the maximum of a minimum of a function.All machine learning and artificial intelligence algorithm used optimization techniques. Lagrange's multiplier is one of the most used optimization technique in mathematics. the role of an optimization technique in STEM is very vital.