Faced with budget constraints and nutritional needs, a high school seeks to devise a daily meal plan. They need to balance minimum nutritional requirements$-500$ calories, $6oz$ of chocolate, $10oz$ of sugar, and $8oz$ of fat $-$ against cost constraints $($Table below$)$; the challenge lies in optimizing food options to effectively meet both criteria.

a$.$ Show the LP formulation for the problem.

b$.$ How can you create a daily meal plan that meets the minimum nutritional requirements of at least $500$ calories, $6oz$ of chocolate, $10oz$ of sugar, and $8oz$ of fat while minimizing costs using Excel solver?

c$.$ What happens when the requirement for calories is reduced to $400?$