(a) Formulate a Mixed Integer Problem (MIP) model: present decision variables, objective function, and constraints.

(b) Solve analytically in Excel Solver.

2. [60 points] The Party Town Company is contracted to produce three new products. Setting up the production facilities to begin production would cost $50,000 for Product 1,$65,000 for Product 2 , and $80,000 for Product 3 . Once these investment costs are covered, the new products would generate a unit profit of $10 (Product 1), $13 (Product 2), and $15 (Product 3 ). The Company has two factories that are capable of producing these products. Product 1 can be produced at the rate of 50 per hour in factory 1 and 40 per hour in factory 2 . Product 2 can be produced at the rate of 25 per hour in factory 1 and 40 per hour in factory 2 . Product 3 can be produced at the rate of 40 per hour in factory 1 and 20 per hour in factory 2 . Factory 1 and 2 have 600 and 730 hours of production time available. Management needs to determine how many units (if any) of each new product should be produced to maximize the net profit