Walker Entertainment is a distributor of video games and expects its video game sales to$.$ be as follows for the first $4$ months of $2017$:

January

February

March

April

$$100,000$

$$150\mathrm{.}000$

$$180,000$

$$200,000$

Walker's cost of goods sold is $70\%$ of sales. Ending inventory is expected to equal $40\%$ of the next month's cost of goods sold. How much are budgeted inventory purchases for February?

A$)$ $$105,000$

B$)$ $$113\mathrm{.}400$

C$)$$$117\mathrm{.}000$

D$)$ $$50,400$