Grouper Cheese Company has developed a new cheese slicer called Slim Slicer. The company plans to sell this slicer through its online website. Given market research, Grouper believes that it can charge $$20$ for the Slim Slicer. Prototypes of the Slim Slicer, however, are costing $$23.$ By using cheaper materials and gaining efficiencies in mass production, Grouper believes it can reduce Slim Slicer's cost substantially. Grouper wishes to earn a return of $20\%$ of the selling price.$($a$)$Compute the target cost for the Slim Slicer.