A toy manufacturer has developed two new toys for possible inclusion in its product line for the upcoming Christmas season. Setting up the production facilities to begin production would cost $50,000 for toy 1 and $80,000 for toy 2. Once these costs are covered, the toys would generate a unit profit of $10 for toy 1 and $15 for toy 2.

The company has two factories that are capable of producing these toys. However, to avoid doubling the start-up costs, just one factory would be used and the choice would be based on maximising 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 man-hour in factory 1 and 40 per man-hour in factory 2. Toy 2 can be produced at the rate of 40 per man-hour in factory 1 and 25 per man-hour in factory 2. Factory 1 and 2, respectively, has 150,000 and 300,000 man-hours of production time available before Christmas that could be used to produce these toys.

It is not known whether these two toys would be continued after Christmas. Therefore, the problem is to determine how many units (if any) of new toy should be produced before Christmas in order to maximise the total profit. Formulate an integer programming model for this problem.