A Snow Cone Stand Sells Three Sizes of Snow Cones $\vec{N}=(56,140,83)$

Short Answer

A snow cone stand sells three sizes of snow cones: small, medium, and large. Let $\vec{N}=(56,140,83)$ give the number of each type of cone sold in one day. Let $\vec{P}=(1.50,2.00,2.50)$ give the price (in dollars) charged for each size of snow cone, $\vec{C}=(0.30,0.40,0.50)$ give the cost (also in dollars) of making each size of snow cone, and $M=(150,200,200)$ give the maximum number of each size that can be sold (because of the number of each size cup on hand.) What is the total number of cups left in the stand at the end of the day?