Problem:

The Toys-R-4-U Company has developed two new toys for possible inclusion in its product line. Setting up the production facilities to begin production would cost $50,000 for toy 1 and $80,000 for toy 2 and the toys would generate a unit profit of $10 for toy 1 and $15 for toy 2.

The company has 2 factories that are capable of producing these toys. However, to avoid doubling the start-up costs, just one factory would be used, where the choice would be based on maximizing profit. For administrative reasons, the same factory would be used for both new toys if both are produced.

Toy 1 can be produced at the rate of 50 per hour in factory 1 and 40 per hour in factory 2. Toy 2 can be produced at the rate of 40 per hour in factory 1 and 25 per hour in factory 2. Factories 1 and 2, respectively, have 500 hours and 700 hours of production time available that could be used to produce these toys.

The problem is to determine how many units (if any) of each new toy should be produced to maximize the total profit.

Required:

Question 1) Formulate an MIP model for this problem.

Question 2) Solve the problem using GAMS and state the optimal solution.

Provide correct solution of the given problem with step by step calculations.