The correct answer is: A. relationship among two or more variables in a straight line
Linear programming is a mathematical method for finding the optimal (best) solution to a problem in a situation where certain conditions must be met. The word “linear” in linear programming refers to the fact that the relationships between the variables in the problem are linear. This means that the variables can be represented by straight lines.
For example, suppose you have a problem where you need to find the best way to mix three ingredients to make a product. The ingredients have different costs, and you want to minimize the cost of making the product. You can represent this problem as a linear program by letting $x_1$, $x_2$, and $x_3$ be the amounts of the three ingredients used, and letting $y$ be the cost of the product. The constraints in the problem would be that the amounts of the ingredients must add up to 1, and that the cost of the product must be less than or equal to some maximum value. The objective of the problem would be to minimize $y$.
The solution to a linear programming problem can be found using a variety of methods, including the simplex method. The simplex method is an algorithm that finds the optimal solution to a linear program by iteratively moving from one feasible solution to another until the optimal solution is reached.
Linear programming is a powerful tool that can be used to solve a variety of problems in a variety of fields. It is used in business, economics, engineering, and many other areas.
Here are brief explanations of each option:
- Option B: A relationship among two or more variables which are directly proportional is not necessarily linear. For example, the relationship between the number of hours you study and your test score is not linear. If you study for 1 hour, you will not get twice the score as if you studied for 0.5 hours.
- Option C: A relationship among two or more variables is not necessarily linear. For example, the relationship between the temperature and the volume of a gas is not linear. As the temperature increases, the volume of the gas increases, but not in a linear fashion.
- Option D: Option A is the only correct option. Option B, C, and D are all incorrect.