Use graphical methods to solve the linear programming problem:
-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) 18 counselors and 12 aides
C) 12 counselors and 18 aides
D) 27 counselors and 18 aides

Question

Quizplus · Accepted Answer

The constraints are: x + y ≤ 45, x + y ≥ 30, y ≥ 10, y ≤ (3/2)x. The objective is to minimize 2400x + 1100y. Solving graphically, the feasible region is bounded by these constraints, and the minimum cost occurs at the point (12, 18).

Use Graphical Methods to Solve the Linear Programming Problem