(a) A set of solar experiments is to be made at observatories. Each experiment begins on a given day of the year and ends on a given day (each experiment is repeated for several years). An observatory can perform only one experiment at a time. The problem is: what is the minimum number of observatories required to perform a given set of experiments annually? Model this scheduling problem as a graph-coloring problem.

(b) Suppose experiment A runs from Sept. 2 to Jan. 3, experiment B from Oct. 15 to March 10, experiment C from Nov. 20 to Feb. 17, experiment D from Jan. 23 to May 30, experiment E from April 4 to July 28, experiment F from April 30 to July 28, and experiment G from June 24 to Sep.30. Draw the associated graph and find a minimal coloring (show that fewer colors will not suffice).