Math Problem Statement

Ketika harga barang Rp16.000 per unit, permintaan Rudi sebanyak 18 unit. Namun, ketika harga barangnya Rp14.000 per unit, maka permintaan Rudi menjadi 22 unit. Berapakah fungsi permintaan Rudi?

Solution

The image you uploaded contains a mathematical question in Indonesian. Here's a translation of the problem:

"When the price of an item is IDR 16,000 per unit, Rudi demands 18 units. However, when the price of the item becomes IDR 14,000 per unit, Rudi demands 22 units. What is the demand function of Rudi?"

To find the demand function, we can assume it follows a linear relationship. A typical demand function takes the form:

Q=abPQ = a - bP

Where:

  • QQ is the quantity demanded,
  • PP is the price,
  • aa and bb are constants.

We know two points on this demand curve:

  1. When P=16,000P = 16,000, Q=18Q = 18,
  2. When P=14,000P = 14,000, Q=22Q = 22.

We can substitute these values into the equation to solve for aa and bb.

Let's calculate the demand function for Rudi. sympy import symbols, Eq, solve

Define variables

P, Q, a, b = symbols('P Q a b')

Define the equation for demand function

demand_eq = Eq(Q, a - b * P)

Substituting the first point (P = 16000, Q = 18)

eq1 = demand_eq.subs({P: 16000, Q: 18})

Substituting the second point (P = 14000, Q = 22)

eq2 = demand_eq.subs({P: 14000, Q: 22})

Solve the system of equations for a and b

solution = solve((eq1, eq2), (a, b)) solutionThe demand function for Rudi is:

Q=501500PQ = 50 - \frac{1}{500} P

Where:

  • QQ is the quantity demanded,
  • PP is the price per unit.

This function shows that as the price increases, the demand decreases. Let me know if you would like more details or have any questions!

Here are some related questions you may find interesting:

  1. How does a price increase affect the quantity demanded in a linear demand function?
  2. How can you determine the elasticity of demand from a linear demand function?
  3. What would happen to the demand if the price reached IDR 0 in this case?
  4. Can demand functions have other forms, such as exponential or logarithmic?
  5. How do shifts in supply influence the demand curve?

Tip: To analyze real-world data, plotting the demand curve can visually show how price changes impact demand!

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Math Problem Analysis

Mathematical Concepts

Linear Functions
Demand Functions
Algebra

Formulas

Q = a - bP

Theorems

Linear equation solving
Demand function interpretation

Suitable Grade Level

Grades 9-12