The CFO for the Shelton Corporation has $1.2 million to allocate to the following budget requests from 5 departments: Dept 1 Dept 2 Dept 3 Dept 4 Dept 5 $450,000 $310,000 $275,000 $187,500 $135,000 Because the total budget requests exceed the available $1.2 million, not all the requests can be satisfied. Suppose that the CFO considers the requests for departments 2 and 3 to be twice as important as those from departments 4 and 5, and the request from department 1 to be twice as important as those from departments 2 and 3. Further suppose that the CFO wants to make sure each department receives at least 70% of the requested amount.
a. Formulate a GP model for this problem.
b. Implement your model and solve it. What is the optimal solution?
c. Suppose the CFO is willing to allocate more than $1.2 million to these budgets but regards exceeding the $1.2 million figure as being twice as undesirable as not the optimal solution?
d. Suppose the CFO regards all deviations from the original budget amounts (including the $1.2 million available) to be equally undesirable. What solution minimizes the maximum percentage deviation from the budgeted amounts?