Objective Function in Linear Programming:
The objective function in a linear programming problem represents the quantity that needs to be maximized or minimized. It is typically denoted by 'z' and is a linear combination of decision variables with coefficients representing the contribution of each variable to the overall objective.

Correct Expression for Objective Function:
The correct expression for an objective function in a Linear Programming Problem is typically a linear combination of decision variables. In this case, the correct expression given is:

z = 3x1 + 10x2
Here, 'z' represents the objective function to be optimized, 'x1' and 'x2' are the decision variables, and 3 and 10 are the coefficients of these variables respectively. This expression indicates that the objective function is a linear combination of 'x1' and 'x2' with specific coefficients attached to each variable.

Explanation:
- The objective function in a Linear Programming Problem is crucial as it defines the goal of the optimization process.
- In the given expression, 'z = 3x1 + 10x2', the coefficients 3 and 10 indicate the contribution or weight of each decision variable towards the objective.
- By maximizing or minimizing this objective function subject to certain constraints, optimal values of the decision variables 'x1' and 'x2' can be determined.
- The objective function plays a key role in guiding the optimization algorithm towards finding the best solution that satisfies all constraints while optimizing the objective.
In conclusion, the correct expression for an objective function in a Linear Programming Problem is a linear combination of decision variables, with specific coefficients representing the contribution of each variable towards the overall objective.