A chain of service facilities (like automobile repair shops) has locations in three cities: A, B, C. Each facility sells two products: 1, and 2. The demand per week at each location is displayed below
A B C
Product1 200 100 100
Product2 300 180 90
These figures give the maximum demand at each location. It is perfectly possible for the firm to sell less than the maximum if it can’t supply potential customers who will then buy from a local competing firm instead.
Product 1 nets $21.50 per unit and product 2 nets $7.25 per unit. These figures are calculated net of the costs of unskilled labor (which is hired locally as required) and net of the costs of incidentals such as tools, equipment, and various other inputs.
Output at each service facility is limited by the number of work stations available. The numbers of stations at each location are: A – 6 workstations, B- 4 workstations, and C –4 workstations.
Each workstation can be used at most 40 hours per week. Product1 requires 0.75 workstation hours per unit. Product2 requires 0.5 workstation hours per unit.
The operation of the chain further relies on the presence of technical management consultants. These management consultants travel between the locations. A total of 250 management consultant hours per week are available for the entire chain. Product1 requires 0.5 management consultant hours per unit. Product2 requires 0.2 management hours per unit. Management is not paid a fixed wage; instead, it is paid a commission based on the joint returns of the entire chain. Therefore, the cost for management is calculated after the process is optimized.
The objective is to maximize revenues of this chain.
1. Give a LP tableau formulation of the above problem
2. Give a mathematical formulation of this problem using summation notation. Clearly define all your variables and sets.
3. Code and solve this problem in GAMS using summation notation. Make sure to use sets. Turn in:
a. Your code
b. Solution report. DO NOT turn in the whole *.lst file. Give a summary of your optimal solutions, shadow prices, and reduced costs.
c. Provide and interpretation of your optimal solutions and shadow prices.