Formulate an integer programming model

Question

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

1. 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
2. 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

Question 2:

 

Ryan Electronics produces electrical components at two production facilities in Denver and Atlanta.  Components produced at either facility are shipped to the firm's supplies retail outlets in Kansas, Louisville, and Dallas.  Following table show the transportation unit costs, supply, and demand at each of the nodes. 

 

Unit Transportation Costs, Demands, and Capacities

Plant/WH	Kansas	Louisville	Dallas	Supply
Denver	$2	$6	$3	700
Atlanta	$4	$4	$6	300
Demand	200	150	350

 

In addition to the unit transportation costs, shipments from plants to warehouses incur fixed costs with the trucking company as show below: Fixed Trucking Costs Unit

Plant/WH	Kansas	Louisville	Dallas
Denver	$2000	$4000	$3500
Atlanta	$1500	$2300	$4000

 

1. 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