Stage Co$.$ is a company specializing in designing stages for Broadway shows. Currently, the client contacted the company regarding the upcoming show and the stage should be ready for rehearsal in a week. The company knows $3$ temporary workers $($Amy$,$ Dave, and Flora$)$ who can immediately join the project. Based on their abilities and experience, the company will pay $$35$ per hour to Amy, $$30$ per hour to Dave, and $$50$ per hour to Flora. Amy can work up to $30$ hours per week, Dave can work up to $35$ hours per week, and Flora can work up to $50$ hours per week. Since Flora is a highly skilled artist the company wants to hire her for at least $10$ hours. The stage manager estimated that $60$ hours extra hours of temporary workers is needed to prepare for the rehearsal. What should be the optimal hiring plan for Stage Co$.$ to minimize the cost?