Alliance Company budgets production of $28,000$ units in January and $32,000$ units in February. Each finished unit requires $4$ pounds of raw material $K$ that costs $$2\mathrm{.}00$ per pound. Each month's ending raw materials inventory should equal $50\%$ of the following month's budgeted materials. The January $1$st inventory for this material is $56,000$ pounds. What is the budgeted materials cost for January?

a$.$ $$112,000$

b$.$ $$168,000$

c$.$ $$240,000$

d$.$ $$120,000$