Dept.

$1$

$$ Dept.

$2$

$$ Dept.

$3$

$$ Dept.

$4$

$$ Dept.

$5$

$

$4$

$5$

$0$

$,$

$0$

$0$

$0$

$$$

$2$

$1$

$0$

$,$

$0$

$0$

$0$

$$$

$2$

$8$

$5$

$,$

$0$

$0$

$0$

$$$

$1$

$9$

$7$

$,$

$5$

$0$

$0$

$$$

$1$

$2$

$8$

$,$

$0$

$0$

$0$

A company has $

$1$

$.$

$2$

$$million to allocate to the following budget requests from five departments:

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

$4$

$$to be twice as important as those from departments

$3$

$$and

$5$

$,$

$$and the request from department

$1$

$$to be twice as important as those from departments

$2$

$$and

$4$

$.$

$$Further$,$ suppose the CFO wants to make sure each department receives at least

$7$

$0$

$\%$

$$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 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 for department

$1$

$.$

$$What is the optimal solution?

d

$.$

$$Suppose 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?