Suppose a company has created the following production budget:

Month Budgeted Production

February $45,000$ units

March $75,000$ units

April $60,000$ units

May $80,000$ units

Each unit produced requires $4$ pounds of direct materials. Management wants to have a direct

materials inventory on hand at the end of each month that is $50\%$ of the following month$$s

production needs. January$$s ending inventory of direct materials is expected to be $90,000$

pounds. It takes $45$ minutes for an assembly line worker to produce each unit, and the assembly

line workers are paid $$20$ per hour.

How many pounds of direct materials should the company plan to purchase in February, March,

and April? Please provide full explanation....