Question

a firm uses 44,900 widgets per year and can produce 350 per day. carrying costs are $ 2 and setup costs are $175. they operate 240 days per year . what is the optimal run size ? do not round intermediate calculations. round your answer to a whole number.

Answer 1

The question deals with calculating the optimal production quantity using the Economic Order Quantity formula. The calculated optimal run size for the firm, given its annual demand, setup cost, and carrying cost, is 2,804 units when rounded to the nearest whole number.

Step-by-step explanation:

The subject question is concerned with finding the optimal run size for a firm that uses 44,900 widgets per year and operates 240 days per year.

The calculation for optimal production quantity can be found using the Economic Order Quantity (EOQ) formula: \( EOQ = \sqrt{\frac{2DS}{H}} \), where \(D\) is the annual demand, \(S\) is the setup cost, and \(H\) is the carrying cost per unit. In this case, we can insert the values \(D = 44,900\) widgets, \(S = $175\) setup cost, and \(H = $2\) carrying cost into the EOQ formula.

Therefore, we calculate the EOQ as:

\( EOQ = \sqrt{\frac{2 \times 44,900 \times 175}{2}} = \sqrt{\frac{15,715,000}{2}} = \sqrt{7,857,500} = 2,804.19 \). Hence, the optimal run size is 2,804 units (rounded to the nearest whole number).