A single doughnut production facility is needed to meet the daily delivery demands of four markets, all of which are at intersections in a road system that has been constructed as a grid. The locations and daily demands of these four markets are shown below. The coordinates are measured in miles from an origin at $(0,0).$ Demands are given in dozens of doughnuts to be delivered each day. MarketCoordinatesDaily DemandAnthill$(8,6)10$Bay$(4,12)15$Cropper$(3,2)10$Downtown$(9,6)6$ a$.$ If the production facility were located at Cropper, what would the rectilinear load$-$distance score be for the daily deliveries?b$.$ Using the center of gravity method, identify the coordinates where the production facility should be located in order to minimize the load$-$distance score.c$.$ What is the rectilinear load$-$distance score for the daily deliveries based on the location found by the center of gravity method in part b$?$d$.$ Based on rectilinear distances, what is the distance from the location found by the center of gravity method to the market that is furthest away from it$?$