12 Class Math Exercise 5.3 Question No.1 To 6 || 2nd Year Mathematics Exercise 5.3 Question 1 To 6

12 Class Math Exercise 5.3 Question No.1 To 6 || 2nd Year Mathematics Exercise 5.3 Question 1 To 6

Welcome to this comprehensive video on linear inequalities in two variables and linear programming in intermediate math! In this video, we will explore:

12 Class Math Ex.5.1 Q.no.1
12 Class Math Ex.5.1 Q.no.2
12 Class Math Ex.5.1 Q.no.3
12 Class Math Ex.5.1 Q.no.4
12 Class Math Ex.5.1 Q.no.5
12 Class Math Ex.5.1 Q.no.6
12 Class Math Ex.5.2 Q.no.1
12 Class Math Ex.5.2 Q.no.2
12 Class Math Ex.5.3 Q.no.1
12 Class Math Ex.5.3 Q.no.2
12 Class Math Ex.5.3 Q.no.3
12 Class Math Ex.5.3 Q.no.4
12 Class Math Ex.5.3 Q.no.5
12 Class Math Ex.5.3 Q.no.6
1. _Linear Inequalities in Two Variables_: Understanding inequalities involving x and y.
2. _Corner Point_: Finding the corner points of a feasible region.
3. _Feasible Region_: Identifying the region that satisfies all constraints.
4. _Feasible Solution_: Finding solutions that satisfy all constraints.
5. _Feasible Solution Set_: Understanding the set of all feasible solutions.
6. _Convex Region_: Identifying regions that are convex.
7. _Objective Function_: Understanding the function to be maximized or minimized.
8. _Optimal Solution_: Finding the maximum or minimum value of the objective function subject to constraints.

We'll solve examples from Ex. 5.3, questions 1 to 6, covering Punjab, KPK, and Federal Board syllabi.

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_Section 1: Linear Inequalities in Two Variables_

A linear inequality in two variables is an inequality involving x and y. It can be written in the form:

ax + by less than c or ax + by greater than c

Where a, b, and c are constants.

_Section 2: Corner Point_

A corner point is a point where two or more constraints intersect. It is also known as a vertex.

_Section 3: Feasible Region_

A feasible region is the region that satisfies all constraints. It is also known as the solution region.

_Section 4: Feasible Solution_

A feasible solution is a solution that satisfies all constraints.

_Section 5: Feasible Solution Set_

A feasible solution set is the set of all feasible solutions.

_Section 6: Convex Region_

A convex region is a region that is convex, meaning that it does not have any indentations.

_Section 7: Objective Function_

An objective function is a function that needs to be maximized or minimized.

_Section 8: Optimal Solution_

An optimal solution is the maximum or minimum value of the objective function subject to constraints.