The Widget Division factory purchases $25,000$ couplers per year for use in its widget manufacturing process. The Director of Purchasing has determined that it costs $$20\mathrm{.}00($in personnel and computer time$)$ for the company to process an order to purchase couplers. It costs the company $$4\mathrm{.}00$ per year to carry a coupler in inventory $($including space allocation, breakage, theft, insurance$).$ As the new Assistant to the Director of Purchasing, your job is to calculate how many couplers should be ordered each time. If you order $100$ couplers at a time, orders will be arriving almost daily so you will have low carrying costs but you will have to pay for processing the $250$ purchases in the year. If you order $100,000$ couplers at a time, you will have low purchase costs but very high inventory carrying costs. The Economic Order Quantity $($EOQ$)$ is the amount that should be ordered each time to minimize the total $($order plus carry$)$ cost$.$ The EOQ is calculated by $(2$DO$/$C$)$ where D is the annual demand, O is the cost to process an order, and C is the annual carrying cost for a unit in inventory. a$)$ Create a worksheet for determining the Economic Order Quantity. Your worksheet should work for any quantities entered. $($Note that the square root of a quantity can be calculated by raising the quantity to the $0\mathrm{.}5$ power.$)$ How many couplers should be purchased at a time?