Find the minimum and maximum values of the objective function and the points where they occur, subject to the constraints x ≥ 0,

y ≥ 0,

x + 5y ≤ 25,

x + y ≤ 18,
and
2x + 2y ≤ 12.
z = x + 6y
The minimum value of
occurs at
(x, y) =

.
The maximum value of
occurs at
(x, y) =

.

Identify a1 and r for the geometric sequence an= -256(-1/4) n-1

Consider that lines b and c are parallel. what is the value of x? what is the measure of the smaller angle?

(b) suppose that consolidated power decides to use a level of significance of α = .05, and suppose a random sample of 100 temperature readings is obtained. if the sample mean of the 100 temperature readings is x⎯⎯ = 60.990, test h0 versus ha and determine whether the power plant should be shut down and the cooling system repaired. perform the hypothesis test by using a critical value and a p-value. assume σ = 5. (round your z to 2 decimal places and p-value to 4 decimal places.)