A dietician is planning a snack package of fruit and nuts. Each ounce of fruit will supply zero units of protein, $3$ units of carbohydrates, and $2$ units of fat, and will contain $20$ calories. Each ounce of nuts will supply $4$ units of protein, $2$ units of carbohydrates, and $4$ units of fat, and will contain $50$ calories. Every package must provide at least $12$ units of protein, at least $12$ units of carbohydrates, and no more than $22$ units of fat. Find the number of ounces of fruit and number of ounces of nuts that will meet the requirement with the least number of calories. What is the least number of calories?

Let $x$ be the ounces of fruit and $y$ be the ounces of nuts. What is the objective function that must by minimized?

$z=x+y$