A hospital ER needs to keep doctors on call, so that a qualified individual is available to perform every

medical procedure that might be required $($there is an official list of such procedures$).$ For each of

several doctors available for on$-$call duty, the additional salary they need to be paid, and which

procedures they can perform, is known. The goal to choose doctors so that each procedure is covered,

at a minimum cost. Doctors list and their ability to perform the procedures are given below. Salaries for

doctors are $300$$$,400$$$,330$$$,290$$$,410$$$,$ and $420$$ respectively.