A bank$$s economist is interested in developing a function to predict Output at each branch. Each

branch has three inputs $($Labor Hours $[$x$1],$ Operating Expenses $[$x$2],$ and Capital Expenses $[$x$3]),$

which are the resources utilized; the current inputs at each branch, along with the actual Output

value, are shown in the table below. The economist has developed a fitted curve function based

on the three inputs, along with four coefficients $($a$0,$ a$1,$ a$2,$ a$3),$ as follows: $=01$

$12$

$23$

$3,$

where Q is the predicted level of Output. The economist wants to fit the model to the actual

Output as best as possible, minimizing the sum of errors subject to the requirement that the

predicted value $($Q$)$ must be greater$-$than$-$equal$-$to the actual Output value. Additionally, assume

the coefficients can be negative for this model.

Branch Labor Hours

$($x$1)$

Operating Expenses

$($x$2)$

Capital Expenses

$($x$3)$ Output

$134,5156,543591289,130$

$249,96011,830550506,808$

$320,6523,464427143,653$

$449,0247,603478385,421$

$536,9238,723830253,525$

$628,9674,606474219,992$

$728,4527,425182193,284$

$845,9118,013790257,253$

$926,89014,662447173,266$

$1047,3767,576764326,752$

$1157,91312,035875478,533$

$1243,4777,2551,109337,643$

$2$

$1349,78610,909405244,127$

$1430,0454,264479139,447$

$1556,5798,895840380,206$

$1643,82412,690801178,769$

$1733,8234,143381216,168$

a$.$ Construct this NLP model and solve using Analytic Solver$$s GRG Nonlinear Engine.

o Label this worksheet Problem $1$

b$.$ Answer the following questions about the solution on the same worksheet as your model:

i$.$ For which branch$($es$)$ is $($are$)$ the model predicting accurately?

ii$.$ Which branch is underperforming most according to the model?