Soal Cerita Program Linear || Menentukan Nilai Optimum dengan Metode Uji Titik Pojok

Summary

This video tutorial explains how to apply optimization techniques to maximize profits when selling cakes. The presenter walks through a real-life example involving the purchase and sale of two types of cakes, 'kue bika' and 'kue serabi.' By setting up a mathematical model with constraints, the speaker demonstrates how to calculate the maximum possible profit given a fixed budget and purchasing limits. Using linear programming and graphical methods, the lesson covers creating objective functions and solving the system of inequalities to determine the optimal number of cakes to sell. The maximum profit of Rp50,000 occurs when selling 100 'kue bika' and 100 'kue serabi.'

Takeaways

• 😀 The lesson explains how to use optimization to maximize profits in a real-life scenario involving cake sales.
• 😀 The two cakes being sold are 'kue bika' (cake 1) and 'kue serabi' (cake 2), with different buying and selling prices.
• 😀 The available budget for buying cakes is Rp150,000, and only 200 cakes can be purchased in total.
• 😀 The goal is to determine how many of each type of cake should be sold to achieve the maximum profit.
• 😀 The mathematical model used involves setting up an objective function to represent profit and constraints based on the available budget and maximum quantity of cakes.
• 😀 'Kue bika' (cake 1) has a cost of Rp1,000 and is sold for Rp1,300, resulting in a profit of Rp300 per cake.
• 😀 'Kue serabi' (cake 2) has a cost of Rp500 and is sold for Rp700, resulting in a profit of Rp200 per cake.
• 😀 Constraints are established based on the budget and the maximum number of cakes, leading to a system of inequalities to model the problem.
• 😀 The optimization problem is solved graphically by finding the feasible region, identifying corner points, and evaluating the objective function at these points.
• 😀 The maximum profit of Rp50,000 is achieved when 100 'kue bika' and 100 'kue serabi' are sold, demonstrating the use of linear programming to solve real-world business problems.

Q & A

What is the objective of the video?

The video aims to teach how to solve optimization problems using the method of testing the optimal point (titik optimum) in real-life scenarios, specifically applying it to a business problem involving selling cakes.

What types of cakes are involved in the problem?

The cakes involved are kue bika and kue serabi.

What are the costs and selling prices of the cakes?

The cost of one kue bika is Rp1000, and it is sold for Rp1300. The cost of one kue serabi is Rp500, and it is sold for Rp700.

What is the total capital available for buying cakes?

The total capital available for purchasing the cakes is Rp150,000.

What is the maximum number of cakes that can be bought?

A maximum of 200 cakes can be purchased in total.

How are the number of kue bika and kue serabi represented in the model?

The number of kue bika is represented by the variable 'x', and the number of kue serabi is represented by 'y'.

What is the objective function in this optimization problem?

The objective function is the total profit, which is 300x + 200y, where x and y are the quantities of kue bika and kue serabi, respectively.

What are the constraints in the optimization model?

The constraints are: 2x + y ≤ 300 (total cost constraint), x + y ≤ 200 (quantity constraint), x ≥ 0, and y ≥ 0 (non-negativity constraints).

How do you determine the feasible region in the graph?

The feasible region is determined by plotting the constraints as lines on the graph and identifying the area that satisfies all of them, specifically the area that is above the x-axis and y-axis.

What is the solution to the optimization problem?

The maximum profit of Rp50,000 occurs when 100 kue bika and 100 kue serabi are sold.