Find the eigenvalues and associated eigenvectors of the following 3x3 matrices. Is there a set of linearly independent eigenvectors? 1 0 0 I K) 1 1 a. A = -1 0 1 b. A = -1 2 -1 (N -1 -1 2 c. A = 2 I 1 1 2 1 1 1 2 d. A = 2 0 0 1 3 0 I 1

L16 - 9 3) Find the actual cost of producing the 101st item given C(101) = 1000 + 25(101) − 0.1(101) =2 04 .90. Now suppose that the unit price p at which x items will sell can be modeled by the demand function p(x)= −0.3x +1 2,0 ≤ x ≤ 400. 4) Find the revenue from the sale of x items. 5) Find the proﬁt function, P(x), which gives the proﬁt from the sale of x items. 6) Estimate the marginal proﬁt when 50 items are sold. Note: P(51) − P(50) = 3579.80 − 3500.