Marisa needs to hire at least 10 staff members for an upcoming project. The staff members will be made up of junior directors, who will be paid \($640\) per week, and senior directors, who will be paid \($880\) per week. Her budget for paying the staff members is no more than \($9,700\) per week. She must hire at least 3 junior directors and at least 1 senior director. Which of the following systems of inequalities represents the conditions described if \(x\) is the number of junior directors and \(y\) is the number of senior directors?

A. \(640x + 880y \geq 9,700\)
\(x + y \leq 10\)
\(x \geq 3\)
\(y \geq 1\)

B. \(640x + 880y \leq 9,700\)
\(x + y \geq 10\)
\(x \geq 3\)
\(y \geq 1\)

C. \(640x + 880y \geq 9,700\)
\(x + y \geq 10\)
\(x \leq 3\)
\(y \leq 1\)

D. \(640x + 880y \leq 9,700\)
\(x + y \leq 10\)
\(x \leq 3\)
\(y \leq 1\)