Company X produces batches of different types of condiments using the same facility. When a sequence of production is completed, a new cycle is started in the same order. The production line needs to be cleaned and sanitized when switching from one product to another. Therefore, product sequencing affects the line sanitation time between successive batches. For instance, the time required to switch from mayonnaise to ketchup is longer than the preparation time to switch from ketchup to mustard due to the existence of allergens in mayonnaise. Let us denote each condiment by (), the number of condiments the company produces by N, and the preparation time to switch from product i to j by , . The preparation time to start the production of the first product and sanitation of the line at the end of the cycle are denoted by () and () , respectively. Assuming that all products are produced in each cycle, the production manager is looking for selecting the product sequence that minimizes the total sanitation time per cycle. Formulate this optimization problem by the aid of integer programming. Describe the decision variables, constraints and objective function