Question:
Consider $ {\frac{x}{2} + \frac{y}{4} \geq 1 }$ and $ {\frac{x}{3} + \frac{y}{2} \leq 1 , x , y \geq 0 }$
Then number of possible solutions are :
Consider $ {\frac{x}{2} + \frac{y}{4} \geq 1 }$ and $ {\frac{x}{3} + \frac{y}{2} \leq 1 , x , y \geq 0 }$
Then number of possible solutions are :
Updated On: Jul 6, 2022
- Zero
- Unique
- Infinite
- None of these
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The Correct Option is C
Solution and Explanation
Consider $ {\frac{x}{2} + \frac{y}{4} \geq 1 ,\frac{x}{3} + \frac{y}{2} \leq 1 , x , y \geq 0 }$ convert them into equation and solve them and draw the graph of these equations
we get
$ {y = 1}$ and $ {x = 3/2}$
From graph region is finite but numbers of possible solutions are infinite.
because for different values of x and y we have different or infinite no. of solutions.
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Notes on Linear Programming Problem
Concepts Used:
Linear Programming
Linear programming is a mathematical technique for increasing the efficiency and effectiveness of operations under specific constraints. The main determination of linear programming is to optimize or minimize a numerical value. It is built of linear functions with linear equations or inequalities restricting variables.
Characteristics of Linear Programming:
- Decision Variables: This is the first step that will determine the output. It provides the final solution to the problem.
- Constraints: The mathematical form in which drawbacks are expressed, regarding the resource.
- Data: They are placeholders for known numbers to make writing complex models simple. They are constituted by upper-case letters.
- Objective Functions: Mathematically, the objective function should be quantitatively defined.
- Linearity: The function's relation between two or more variables must be straight. It indicates that the variable's degree is one.
- Finiteness: Input and output numbers must be finite and infinite. The best solution is not possible if the function consists infinite components.
- Non-negativity: The value of the variable should be either positive (+ve) or 0. It can't be a negative (-ve) number.