Lego Toys is planning to produce new toys at its factories.  The setup cost of the production facilities, production costs and profits for each toy are given below:

Toy    Setup cost ($)       Unit Cost ($)        Selling Price ($)
1         45000                    8                       20
2         76000                   11                     25

The company has two factories that are capable of producing these toys. The production rates of each toy are given below (in units/hour):

                Toy 1          Toy 2
Factory 1      52              38
Factory 2      42              23

Factories 1 and 2, respectively, have 480 and 720 hours of production time available for the production of these toys. In addition, each of the toys requires 4 pounds of material and the total material available is 100000 pounds.  The manufacturer wants to know which of the new toys to produce, where and how many of each (if any) should be produced so as to maximize the total profit.

a.    Formulate an integer programming model by identifying decision variables and clearly expressing objective function and constraints as mathematical functions. Solve the problem in EXCEL and discuss the solution
b.    If the company has a restriction that it has to produce at least 400 units of each toy if they are scheduled for production, how does the model change? Express any additional constraints as mathematical expressions.