I need a mathematical solution. step by step one by one.

1. Tank-trucks have several compartments c= 1, ..., n of varying capacity Ue. The final stage of distribution planning is to allocate outgoing gasoline products p = 1,...,m to compartments. The various products ordered are placed in one or more compartments, but each compartment can contain only one product. To avoid overfilling, the total gallons of any product loaded can be reduced from the ordered volume vp by up to bp gallons. The loading procedure seeks to minimize the sum of these underloadings while meeting all other requirements. [20pt] Formulate an IIP model using Xp,c: gallons of product p loaded in compartment c, 1 if product p is loaded in compartment c Yp,c 0 otherwise Zp: gallons underloading of product p. = {