The XYZ Company has developed two new products to potentially add to their product line before the next holiday season. The cost of setting up production facilities for product 1 is $50,000, and for product 2 , it is $70,000. Once the initial costs are recovered, each unit of product 1 generates a profit of $10, and each unit of product 2 generates a profit of $15. The company has two factories that can produce these products, but only one factory can be used to avoid doubling the setup costs. The choice of factory will be based on maximizing profit If both new products are produced, they will be manufactured in the same factory for administrative reasons. In factory 1 , product 1 can be produced at a rate of 50 per hour (or 1/50 hours per unit), and product 2 can be produced at a rate of 40 per hour (or 1/40 hours per unit). In factory 2 , product 1 can be produced at a rate of 40 per hour (or 1/40 hours per unit), and product 2 can be produced at a rate of 25 per hour. Before Christmas, there are 500 hours of production time available in factory 1 and 700 hours of production time available in factory 2 . It is not known whether these products will be continued after the holiday season. Therefore, the objective is to determine the optimal number of units of each product to produce before Christmas to maximize the total profit.

Formulate a MIP (Mixed Integer Programming) model for this problem.