Problem $6.$ Marginal Analysis: Tables. Meredith Grey is a regional sales representative for Dental Laboratories, Inc., a company that sells alloys created from gold, silver, platinum, and other precious metals to several dental laboratories in Washington, Oregon, and Idaho. Grey's goal is to maximize total monthly commission income, which is figured at $8$ percent of gross sales. In reviewing monthly experience over the past year, Grey found the following relations between days spent in each state and monthly sales generated:

$\backslash$table$[[$Washington$,$Oregon,Idaho$],[$Days$,$Gross Sales $($$$),$Days,Gross Sales $($$$),$Days,Gross Sales $($$$)],[0,10,000,0,0,0,6,250],[1,25,000,1,8,750,1,12,500],[2,37,500,2,16,250,2,17,500],[3,47,500,3,22,500,3,21,250],[4,55,000,4,26,250,4,23,750],[5,60,000,5,28,750,5,25,000],[6,62,500,6,30,000,6,25,000],[7,62,500,7,31,250,7,25,000]]$

A$.$ Construct a table showing Grey's marginal sales per day in each state.

B$.$ If administrative duties limit Grey to only ten selling days per month, how should these $10$ days be spent in the three states to maximize commission income?

C$.$ Calculate Grey's maximum monthly commission income.