Park Hae-Soo has a small business that sells sugarcane drinking straws in Melbourne. The business has been successful recently because single use plastic straws are being phased out in Victoria by February 2023. He has a commercial truck that he uses to deliver boxes of sugarcane drinking straws to his customers. The straws come in two types, cocktail straws and boba straws.

His business warehouse has four different storage compartments with capacities to hold 400, 400, 500, 500 boxes of sugarcane drinking straws. Park Hae-Soo received an order today to deliver 1,000 boxes each of straw to a customer. If each storage compartment can hold only up to one type of drinking straw, how should Park Hae-Soo load the storage compartments to meet this demand?

If it is impossible to load what he needs in the compartment to meet the demand, Park Hae- Soo wants to minimise the total number of boxes by which the order is short. Formulate an ILP model for this problem. (Hint: In addition to defining decision variables for the number of boxes to be stored in a compartment and whether or not a straw type is stored in a compartment, you may want to define additional two variables to represent shortage amounts called S1 and S2.)