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Use graphical methods to solve the linear programming problem. 34) 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. How many counselors and how many aides should the camp hire to minimize cost? A) 35 counselors and 10 aides C) 18 counselors and 12 aides B) 12 counselors and 18 aides D) 27 counselors and 18 aides

Use graphical methods to solve the linear programming problem. 34) 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. How many counselors and how many aides should the camp hire to minimize cost? A) 35 counselors and 10 aides C) 18 counselors and 12 aides B) 12 counselors and 18 aides D) 27 counselors and 18 aides

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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```plaintext x₁, x₂ ≥ 0 are O = (0, 0), A = (0, 7), B = (6, 5), and C = (8, 0). Find the optimal solution for the objective profit function: P = 5x₁ + 5x₂ MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Use graphical methods to solve the linear programming problem. 34) 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. How many counselors and how many aides should the camp hire to minimize cost? A) 35 counselors and 10 aides B) 12 counselors and 18 aides C) 18 counselors and 12 aides D) 27 counselors and 18 aides ``` **Graph Explanation:** The linear programming problem involves determining the optimal number of counselors (x₁) and aides (x₂) to minimize cost, given certain constraints. The points O, A, B, and C represent feasible solutions within a graph where the x-axis and y-axis denote the number of counselors and aides, respectively. The profit function P = 5x₁ + 5x₂ suggests maximizing profit, but the problem focuses on staffing cost minimization within the given restrictions.
Transcribed Image Text:```plaintext x₁, x₂ ≥ 0 are O = (0, 0), A = (0, 7), B = (6, 5), and C = (8, 0). Find the optimal solution for the objective profit function: P = 5x₁ + 5x₂ MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Use graphical methods to solve the linear programming problem. 34) 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. How many counselors and how many aides should the camp hire to minimize cost? A) 35 counselors and 10 aides B) 12 counselors and 18 aides C) 18 counselors and 12 aides D) 27 counselors and 18 aides ``` **Graph Explanation:** The linear programming problem involves determining the optimal number of counselors (x₁) and aides (x₂) to minimize cost, given certain constraints. The points O, A, B, and C represent feasible solutions within a graph where the x-axis and y-axis denote the number of counselors and aides, respectively. The profit function P = 5x₁ + 5x₂ suggests maximizing profit, but the problem focuses on staffing cost minimization within the given restrictions.
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