Please use python code: $1-$ Carbon anodes used in a smelting process are baked in a ring furnace. An experiment is

run in the furnace to determine which factors influence the weight of packing material that

is stuck to the anodes after baking. Six variables are of interest, each at two levels: $A=$

pitch$/$fines ratio $(0\mathrm{.}45,0\mathrm{.}55),B=$ packing material type $(1,2),C=$ packing material

temperature $($ambient$,325C),D=$ flue location $($inside$,$ outside$),E=$ pit temperature

$($ambient$,195C),$ and $F=$ delay time before packing $($zero$,24$ hours$).$ A $2^{6-3}$ design is run,

and three replicates are obtained at each of the design points. The weight of packing

material stuck to the anodes is measured in grams. The data in run order are as follows:

abd $=(984,826,936)$; absdef $=(1275,976,1457)$; be $=(1217,1201,890)$; af $,$

$1164,1541$; ace $=(1338,1254,1294)$; and

bcf $=(1325,1299,1253).$ We wish to minimize the amount of stuck packing material.

$($a$)$ Verify that the eight runs correspond to a $2_{\text{I}\text{I}\text{I}}^{6-3}$ design. What is the alias structure?

$($b$)$ Use the MEAN weight as a response. What factors appear to be influential?

$($c$)$ Use the RANGE of the weights as a response. What factors appear to be influential?