Problem $19$S$-4($Algo$)$

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 $2,200$ and $3,800$ calories. No more than $1,600$ calories can be starch, and no fewer than $400$ can be protein. The varied diet is to be made of two foods: A and B$.$ Food A costs $$0\mathrm{.}72$ per pound and contains $800$ calories, $676$ of which are protein and $124$ starch. No more than $2$ pounds of food A can be used per resident. Food B costs $$0\mathrm{.}13$ per pound and contains $1,100$ calories, of which $800$ are starch, $190$ are protein, and $110$ are fat.

a$.$ Write the equations representing this information. $($Round your answers to $2$ decimal places.$)$

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