The Toys-R-U Company has developed two new toys for possible inclusion in its product line for 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 (1) 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 units per hour in Factory 1 and 40 units per hour in Factory 2. Toy 2 can be produced at the rate of 40 units per hour in Factory 1 and 25 units per hour in Factory 2. Factory 1 and Factory 2, respectively, have 500 hours and 700 hours of production time available before Christmas that could be used to produce these toys.
It is not known whether the production of these toys would be continued after Christmas. Therefore the problem is to determine how many units (if any) of each new toy should be produced before Christmas to maximize the total profit.
1. Formulate algebraically a BIP model for this problem. Define the decision variables, objective function, and constraints.
2. Formulate this same BIP problem on a spreadsheet and SOLVE using Excel solver (Provide a printout of the corresponding “Excel Spreadsheet” and the “Answer Report”).
3. Describe clearly and completely the optimal solution to this problem using a managerial statement.