Bonar memiliki dua pekerjaan paruh waktu. Untuk mengantar barang, Bonar dibayar Rp 15.000,00 per ...

Summary

The video explains a mathematical problem involving Bonar's two part-time jobs: delivering goods and washing dishes at a restaurant. The goal is to determine the mathematical model for his working hours and earnings, expressed through linear inequalities. The process involves setting up equations, solving for the feasible region, and graphing the inequalities. The video also answers questions about whether Bonar can meet his financial goals by working specific hours, exploring different scenarios using the derived model. It covers concepts like linear systems, feasible regions, and point intersections, offering a comprehensive guide to solving the problem.

Takeaways

• 😀 Bonar has two part-time jobs: delivering goods, paying Rp15,000 per hour, and washing dishes at a restaurant, paying Rp9,000 per hour.
• 😀 The variables 'x' and 'y' represent the number of hours Bonar spends delivering goods and washing dishes, respectively, and both must be non-negative.
• 😀 The total work hours Bonar can dedicate to both jobs is capped at 10 hours, so the equation is x + y ≤ 10.
• 😀 Bonar needs to earn at least Rp120,000. The combined wages from both jobs must be greater than or equal to Rp120,000.
• 😀 The mathematical model is a system of linear inequalities based on the conditions provided.
• 😀 The system of inequalities describes a linear system because each variable has an exponent of 1, satisfying the definition of linear inequalities.
• 😀 To graph the inequalities, the '≤' signs are replaced with '=' to find the intercepts. The solution region is then determined by the sign of the inequalities.
• 😀 For the first inequality, the feasible region is above the x-axis and to the right of the y-axis.
• 😀 The point (0,0) satisfies the first inequality but not the second, so the feasible solution region lies to the right of the y-axis.
• 😀 The intersection of the two inequalities occurs at the point (5,5), which satisfies both equations.
• 😀 Based on the graph, if Bonar works 4 hours delivering goods, the total earnings wouldn't meet the required Rp120,000, so this is not a feasible solution.
• 😀 If Bonar works 9 hours, there is a feasible solution, and he can earn the required Rp120,000, with possible values for x and y ranging from x ∈ [8, 10] and y ∈ [0, 5].

Q & A

What are the two jobs Bonar has in the story?

Bonar has two part-time jobs: delivering goods, which pays Rp15,000 per hour, and washing dishes in a restaurant, which pays Rp9,000 per hour.

What variables are used to represent Bonar's work hours?

The variable 'x' represents the number of hours Bonar spends delivering goods, and 'y' represents the number of hours spent washing dishes.

What is the mathematical model for the total number of hours Bonar can work?

The mathematical model is represented by the inequality: x + y ≤ 10, where 'x' and 'y' are non-negative numbers, indicating that Bonar cannot work more than 10 hours in total.

How much money does Bonar need to earn?

Bonar needs to earn at least Rp120,000 from both jobs combined.

What is the inequality representing Bonar's earnings?

The inequality representing Bonar's earnings is 15,000x + 9,000y ≥ 120,000, which is simplified to 5x + 3y ≥ 40 after dividing by 3,000.

What type of mathematical system is being used here?

The system described is a system of linear inequalities, as each inequality involves variables raised to the first power.

How is the graph of the inequalities represented?

The graph is represented by two lines where each inequality is treated as an equation. The solution region is the area where both inequalities overlap.

How do we determine the feasible solution region on the graph?

The feasible region is determined by testing points and checking which satisfy both inequalities. For instance, testing the point (0, 0) helps to determine one of the regions.

What is the solution to the system of equations when finding the intersection point of the two lines?

The intersection point of the two lines is (5, 5), found by solving the system using the elimination method.

Can Bonar meet his financial goal if he works 4 hours delivering goods?

No, Bonar cannot meet his financial goal by working 4 hours delivering goods, as this does not fall within the feasible region of solutions for the system of inequalities.