Lastiksan produces different types of tires for trucks. The company considers to develop five possible new tires for automobiles. The management needs to make the decision of which tries to produce and the production amount of these tires. The setup cost of each tire production line and marginal revenues are given in the following table. The management wants to know which tries to produce in order to maximize total net profit.

a) Formulate an IP model for this problem. Define your decision variables clearly.
b) Modify the integer program so that the following conditions are satisfied:
• No more than three types of tires can be produced.
• If tire B is produced then tire A cannot be produced.
• At least two of the following constraints are satisfied:
1. The number of produced tire C must be at least 50.
2. The number of produced tire E must be at most 20.
3. The total number of produced tire D and E must be at most 100.

 

Tire Type C D E Setup Cost Marginal Revenue 60.000 50.000 70.000 80.000 40.000 10 8 11 9 6.