A diet is being prepared for the University of Arizona dorms. The objective is to feed the students at the least cost, but the diet must have between $1,800$ and $3,900$ calories. No more than $1,700$ calories can be starch, and no fewer than $600$ can be protein. The varied diet is to be made of two foods: A and B $.$ Food A costs $$0\mathrm{.}77$ per pound and contains $800$ calories, $701$ of which are protein and $99$ starch. No more than $2$ pounds of food A can be used per resident. Food B costs $$0\mathrm{.}14$ per pound and contains $1,000$ calories, of which $700$ are starch, $140$ are protein, and $160$ are fat.