By graphing the system of constraints and using the values of X and y the minimize the objective function find the minimum value The given text represents a set of linear inequalities and an objective function, typically used in linear programming to find minimum or maximum values under certain constraints.### Constraints:1. $ 25 \leq x \leq 75 $2. $ y \leq 110 $3. $ 8x + 6y \geq 720 $4. $ y \geq 0 $### Objective Function:Minimize $ C = 8x + 5y $### Explanation:- **Variable Ranges**: - $ x $ is constrained between 25 and 75. - $ y $ is constrained to be less than or equal to 110 and greater than or equal to 0.- **Inequality Constraint**: - The inequality $ 8x + 6y \geq 720 $ sets a lower bound on the combined values of $ x $ and $ y $.- **Objective**: - The goal is to find values of $ x $ and $ y $ that minimize the function $ C = 8x + 5y $ within the given constraints.This setup is commonly used for optimization problems where resources, costs, or other factors need to be minimized while satisfying specific conditions.

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Algebra and Trigonometry (6th Edition)

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ChapterP: Prerequisites: Fundamental Concepts Of Algebra

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Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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By graphing the system of constraints and using the values of X and y the minimize the objective function find the minimum value

The given text represents a set of linear inequalities and an objective function, typically used in linear programming to find minimum or maximum values under certain constraints.

### Constraints:
1. $ 25 \leq x \leq 75 $
2. $ y \leq 110 $
3. $ 8x + 6y \geq 720 $
4. $ y \geq 0 $

### Objective Function:
Minimize $ C = 8x + 5y $

### Explanation:
- **Variable Ranges**:
- $ x $ is constrained between 25 and 75.
- $ y $ is constrained to be less than or equal to 110 and greater than or equal to 0.

- **Inequality Constraint**:
- The inequality $ 8x + 6y \geq 720 $ sets a lower bound on the combined values of $ x $ and $ y $.

- **Objective**:
- The goal is to find values of $ x $ and $ y $ that minimize the function $ C = 8x + 5y $ within the given constraints.

This setup is commonly used for optimization problems where resources, costs, or other factors need to be minimized while satisfying specific conditions.

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