Gooding Company manufactures two models of its skillet, the Kitchen and the Campfire. The Kitchen model requires $10,000$ direct labor hours and the Campfire requires $30,000$ direct labor hours. The company produces $3,400$ units of the Kitchen model and $600$ units of the Campfire model each year. The company inspects one Kitchen for every $100$ produced, and inspects one Campfire for every $10$ produced. The company expects to incur $$84,600$ of total inspecting costs this year. How much of the inspecting costs should be allocated to the Kitchen model using ABC costing?

$$ a$.$ $$21,150$

b$.$ $$30,600$

c$.$ $$42,300$

d$.$ $$71\mathrm{.}910$