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For problems 3-5 A math camp wants to hire counselors and aides to fill its staffing needs at minimum cost. The average monthly salary of a counselor is $2400 and the average monthly salary of an aide is $1100. The camp can accommodate up to 45 staff members and needs at least 30 to run properly. They must have at least 10 aides, and may have up to 3 aides for every 2 counselors. 3. Write the system of linear inequalities and the equation to be maximized for the problem above. 4. Graph the system of inequalities and find all the corner points. How many counselors and how many aides should the camp hire to minimize cost? (answer must be in a full sentence)

For problems 3-5 A math camp wants to hire counselors and aides to fill its staffing needs at minimum cost. The average monthly salary of a counselor is $2400 and the average monthly salary of an aide is $1100. The camp can accommodate up to 45 staff members and needs at least 30 to run properly. They must have at least 10 aides, and may have up to 3 aides for every 2 counselors. 3. Write the system of linear inequalities and the equation to be maximized for the problem above. 4. Graph the system of inequalities and find all the corner points. How many counselors and how many aides should the camp hire to minimize cost? (answer must be in a full sentence)

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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### Staffing Problem at a Math Camp A math camp aims to hire counselors and aides to meet its staffing needs at minimum cost. The average monthly salary for a counselor is $2400, while an aide earns $1100. The camp can accommodate a total of 45 staff members and needs at least 30 staff to operate effectively. Additionally, the camp requires at least 10 aides and limits the number of aides to a maximum of 3 for every 2 counselors. #### Tasks: 1. **Formulate Linear Inequalities** - Determine the system of linear inequalities and the cost equation to minimize based on the given constraints and salaries. 2. **Graph the System of Inequalities** - Plot the inequalities on a coordinate plane. - Identify and mark all corner points, which are potential solutions. 3. **Determine the Optimal Staffing Mix** - Calculate the number of counselors and aides the camp should hire to minimize costs. - Provide the answer in a complete sentence. ### Graph Explanation The graph should be a representation of the solution space defined by the linear inequalities. The axes may represent the number of counselors and aides, respectively. The feasible region, where all conditions are satisfied, will be highlighted, and corner points should be labeled as they indicate potential optimal solutions. --- In solving these, you can use methods like linear programming to find the optimal staffing configuration that minimizes costs while satisfying all constraints.
Transcribed Image Text:### Staffing Problem at a Math Camp A math camp aims to hire counselors and aides to meet its staffing needs at minimum cost. The average monthly salary for a counselor is $2400, while an aide earns $1100. The camp can accommodate a total of 45 staff members and needs at least 30 staff to operate effectively. Additionally, the camp requires at least 10 aides and limits the number of aides to a maximum of 3 for every 2 counselors. #### Tasks: 1. **Formulate Linear Inequalities** - Determine the system of linear inequalities and the cost equation to minimize based on the given constraints and salaries. 2. **Graph the System of Inequalities** - Plot the inequalities on a coordinate plane. - Identify and mark all corner points, which are potential solutions. 3. **Determine the Optimal Staffing Mix** - Calculate the number of counselors and aides the camp should hire to minimize costs. - Provide the answer in a complete sentence. ### Graph Explanation The graph should be a representation of the solution space defined by the linear inequalities. The axes may represent the number of counselors and aides, respectively. The feasible region, where all conditions are satisfied, will be highlighted, and corner points should be labeled as they indicate potential optimal solutions. --- In solving these, you can use methods like linear programming to find the optimal staffing configuration that minimizes costs while satisfying all constraints.
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