Please Show the Steps for better learning. 1) Write sin (60t + pi/4) as Re [cos (60t + ?)] . 2) What if no edge exiting from a corner makes a

Please Show the Steps for better learning.

1) Write sin (60t + pi/4) as Re [cos (60t + ?)] . 

2) What if no edge exiting from a corner makes a positive dot product with c ?

3) What if there is no next "corner"? What if there is no limit as to how far we can go?

4)  Maximize the objective function z in the polyhedron defined by

5) Find the minimum-cost order for the Antarctic dietician's specifications.  (Unit 3). Use MATLAB.