$6.$ Coordinating Production and Marketing $(25$ points$)$

The Andrews Apple Products Company purchases apples from local growers and makes applesauce and apple juice. It costs $$0\mathrm{.}70$ to produce a jar of applesauce and $$0\mathrm{.}50$ to produce a bottle of apple juice. The company has a policy that at least $20$ percent but not more than $60$ percent of its output must be applesauce.