Soal Cerita Program Linear

Summary

In this video, the presenter explains how to solve a linear programming problem using a real-world cake-making scenario. A baker needs to maximize revenue while managing constraints on flour and sugar for two types of cakes, *Kue Dadar* and *Kue Apem*. Through the formulation of mathematical models, graphical representation, and solving intersection points, the solution reveals that the maximum revenue of 300,000 IDR is achieved by baking 150 *Kue Dadar* and 100 *Kue Apem*. The video walks through each step in detail, helping viewers understand how to apply linear programming to practical problems.

Takeaways

• 😀 The cake maker has 8,000 grams of flour and 2,000 grams of sugar, and wants to bake two types of cakes: Kue Dadar and Kue Apem.
• 😀 Kue Dadar requires 10 grams of sugar and 20 grams of flour, while Kue Apem requires 5 grams of sugar and 50 grams of flour.
• 😀 Kue Dadar is sold for 1,000 IDR each, and Kue Apem is sold for 1,500 IDR each.
• 😀 The goal is to maximize the total revenue from selling both types of cakes, subject to ingredient constraints.
• 😀 Variables are defined as: X = number of Kue Dadar cakes, Y = number of Kue Apem cakes.
• 😀 The mathematical model consists of two inequalities: 10X + 5Y ≤ 2000 for sugar and 20X + 50Y ≤ 8000 for flour.
• 😀 Additional constraints ensure that both X and Y must be greater than or equal to zero (X ≥ 0, Y ≥ 0).
• 😀 The objective function to maximize is the total revenue: 1000X + 1500Y.
• 😀 The intersection points of the constraints are calculated to determine the feasible region and potential solutions.
• 😀 The corner points of the feasible region are tested by substituting them into the objective function to find the maximum revenue, which is 300,000 IDR with 150 Kue Dadar and 100 Kue Apem.
• 😀 The maximum income of 300,000 IDR is achieved by producing 150 Kue Dadar and 100 Kue Apem cakes.

Q & A

What is the main goal of the linear programming problem discussed in the script?

The main goal is to determine the maximum revenue that a cake maker can earn by making two types of cakes (dadar and apem) using limited amounts of ingredients (flour and sugar).

What ingredients are used to make the cakes in the problem?

The ingredients used are flour and sugar. The cake maker has 8,000 grams of flour and 2,000 grams of sugar.

How much of each ingredient is required for making one dadar cake?

To make one dadar cake, 10 grams of sugar and 20 grams of flour are required.

How much of each ingredient is needed to make one apem cake?

To make one apem cake, 5 grams of sugar and 50 grams of flour are required.

What is the selling price for one dadar cake and one apem cake?

The selling price for one dadar cake is 1,000 IDR, and for one apem cake, it is 1,500 IDR.

What variables are used to represent the number of cakes to be made?

The number of dadar cakes is represented by 'x', and the number of apem cakes is represented by 'y'.

What are the constraints in this linear programming problem?

The constraints are: 10x + 5y ≤ 2,000 (for sugar), 20x + 50y ≤ 8,000 (for flour), and x ≥ 0, y ≥ 0 (non-negativity constraints).

What is the objective function in this problem?

The objective function is to maximize the total revenue, which is represented as: 1,000x + 1,500y.

How do you find the intersection points of the constraints?

You set each of the inequalities as equalities (changing '≤' to '=') and solve the resulting system of linear equations to find the intersection points.

What is the maximum revenue, and how many cakes should be made to achieve it?

The maximum revenue is 300,000 IDR, which is achieved by making 150 dadar cakes and 100 apem cakes.