Math Problem Statement

There are three main questions: (1) Find the maximum value of Z = 30x + 10y under the constraints of a system of inequalities. (2) A fruit seller's optimization problem involving purchasing apples and oranges. (3) Another fruit seller's problem related to maximizing profit with bananas and oranges, given budget constraints.

Solution

It looks like you've uploaded a photo of a math problem related to linear programming or optimization. Here's a breakdown of the key parts I can see:

  1. Question 1 seems to be about finding the maximum value of Z=30x+10yZ = 30x + 10y, given some constraints in a system of inequalities. The options are a. 60, b. 80, c. 100, d. 120, and e. 180.

  2. Question 2 involves a fruit seller buying apples and oranges. The problem likely involves setting up a system of linear inequalities or equations based on price, weight, and budget constraints.

  3. Question 3 also deals with a fruit seller, buying bananas and oranges, where the budget is 1,000,000 Rp and involves maximizing profit given constraints.

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Math Problem Analysis

Mathematical Concepts

Linear Programming
Optimization
Systems of Inequalities
Linear Equations

Formulas

Z = 30x + 10y
Cost = Price per kg * Quantity
Constraints as inequalities

Theorems

Linear programming optimization
Graphical solution method

Suitable Grade Level

Grades 10-12 or early college