The CFO for the Shelton Corporation has $1.2 million to allocate to the following budget requests from five 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 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. Fur- ther suppose 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 meeting the budget request of department 1. What is 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?