A company has $$1\mathrm{.}2$ million to allocate to the following budget requests from five departments:

Dept. $1$ Dept. $2$ Dept. $3$ Dept. $4$ Dept. $5$

$$450,000210,000$ $$285,000$ $$197,500128,000$

Because the total budget requests exceed the available $$1\mathrm{.}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 $70\%$ 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 CFO is willing to allocate more than $$1\mathrm{.}2$ million to these budgets but regards exceeding the $$1\mathrm{.}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\mathrm{.}2$ million available$)$ to be equally undesirable. What solution minimizes the maximum percentage deviation from the budgeted amounts?