How to Solve Business Maths Exercise 5.2 with Ease: 12th Grade Solutions
If you’re a 12th-grade student or someone who is interested in solving business maths exercises, you might have come across the Exercise 5.2, which deals with topics such as Linear Programming and Probability. This exercise can seem challenging, but with the right approach and knowledge, you can solve it with ease.
What is Exercise 5.2?
Exercise 5.2 is a part of the Business Maths textbook for 12th-grade students. This exercise covers topics such as Linear Programming, Probability, etc. It requires students to solve practical problems and apply the concepts learned in these topics.
Understanding the Basic Concepts
To solve Exercise 5.2 with ease, it’s crucial to have a sound knowledge of basic concepts related to Linear Programming and Probability. These include understanding Linear Equations and Inequalities, calculating Profit and Loss, learning Probability Theory, etc.
Step-by-Step Approach to Solve Exercise 5.2
To solve Exercise 5.2, you can follow the below-mentioned steps:
1. Understand the Problem Statement: The first step to solving any problem is to understand the given problem statement correctly. It includes identifying the objective, constraints, and other necessary information.
2. Formulate the Problem: After understanding the problem statement, the next step is to formulate the problem by applying the concepts learned in the topic. You’ll need to represent the problem as Linear Equations or Inequalities.
3. Graph the Problem: Once you’ve formulated the problem, you’ll need to graph it using the coordinate plane. This will help you visualize the problem and come up with an optimal solution.
4. Identify the Feasible Region: After graphing the problem, you’ll need to identify the feasible region, which is the set of all possible solutions that satisfy the constraints in the problem.
5. Find the Optimal Solution: The final step is to find the optimal solution, which maximizes or minimizes the objective function, subject to the given constraints.
Example Problem Solution
To understand the steps involved in solving Exercises 5.2 better, let’s take an example problem:
Maximize Z = 3x + 2y
Subject to:
2x + 3y ≤ 12,
x + y ≥ 3,
x ≥ 0, y ≥ 0
The steps involved in solving this problem are:
1. Understand the Problem Statement: The problem states that we need to maximize Z = 3x + 2y, subject to certain constraints.
2. Formulate the Problem: We can represent the given problem as linear equations and inequalities:
2x + 3y ≤ 12,
x + y ≥ 3,
x ≥ 0, y ≥ 0.
3. Graph the Problem: We can graph the above inequalities on a coordinate plane and identify the feasible region.
4. Identify the Feasible Region: The feasible region for the above problem is the shaded area in the graph bounded by the inequalities.
5. Find the Optimal Solution: To find the optimal solution, we need to evaluate the objective function at each corner point of the feasible region and choose the point that maximizes Z.
By evaluating the objective function at each corner point of the feasible region, we get the following values:
(0, 4) – Z = 8
(3, 0) – Z = 9
(2, 2) – Z = 10
Thus, the optimal solution is (2,2), which maximizes Z = 10.
Conclusion
Solving Business Maths Exercise 5.2 can be a daunting task, but with the right approach and understanding of the basic concepts, you can solve it with ease. Following a step-by-step approach to solving the problems and understanding the feasibility and optimization criteria can help you solve the problems efficiently. So, go ahead and solve Exercise 5.2 with confidence!
