For problems 14c and 14e, derive the chromatic polynomials by hand using the Reduction Theorem and then use MAPLE to reduce and check them. 14. (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). For problems 14c and 14e, derive the chromatic polynomials by hand using the Reduction Theorem and then use MAPLE to reduce and check them. 14. (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)