Question

If the number of available constraints is 3 and the number of parameters to be optimised is 4, then

• A. The objective function can be optimised
• B. The constraints are short in number
• C. The solution is problem oriented
• D. None of the above

Hint:

In optimization problems, the number of constraints should be equal to or greater than the number of parameters to be optimised.

Answer 1

The Correct Option is B

To optimise \(n\) number of parameters, we need at least \(n\) constraints. In this case, there are 3 constraints for 4 parameters, which means the constraints are short in number.

Answer 2

Step 1: Understanding the Problem
In optimization problems, constraints refer to the conditions or limitations that the solution must satisfy. Parameters to be optimized are the variables or quantities that we aim to optimize (maximize or minimize) within the given constraints.
Here, we are given:
- The number of available constraints = 3
- The number of parameters to be optimized = 4
Step 2: Analyzing the Situation
For an optimization problem to be well-posed and solvable, typically the number of constraints should be at least equal to or greater than the number of parameters. If the number of constraints is less than the number of parameters, then there might not be enough conditions to uniquely determine a solution.
In this case, we have 3 constraints and 4 parameters, which means there is one parameter that is not directly constrained by the available conditions.
Step 3: Conclusion
Since the number of available constraints (3) is less than the number of parameters (4), it indicates that the constraints are short in number relative to the parameters to be optimized.
Thus, the correct conclusion is:
The constraints are short in number.