11.11. An experimenter has run a Box–Behnken design and obtained the results as shown in Table P11.5, where the response variable is the viscosity of a polymer:

(a) Fit the second-order model.

(b) Perform the canonical analysis. What type of surface has been found?

(c) What operating conditions on x1, x2, and x3 lead to the stationary point?

(d) What operating conditions would you recommend if it is important to obtain a viscosity that is as close to 600 as possible?

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Level Agitation Temp. Rate Pressure x2 x3 High 200 10.0 25 +1 +1 +1 Middle 175 7.5 20 00 0 Low 150 5.0 15 -1 -1 -1 Run x2 X3 1 0 535 234561 +1 0 580 +1 0 596 +1 +1 0 563 0 645 +1 0 458 7 0 +1 350 8 +1 0 +1 600 9 0 595 10 0 +1 648 11 0 +1 532 12 0 +1 +1 656 13 0 0 0 653 14 0 0 0 599 15 0 0 0 620