**Addressing the EOQ problem** I need to solve the EOQ (Economic Order Quantity) problem with the data provided: annual demand of 12,000 units, ordering cost of $40 per order, and a holding cost of $2 per unit per year. I’ll calculate the EOQ, the number of orders each year, and the length of the order cycle in days. However, the mention of "slack" for activities seems unrelated to EOQ; it likely indicates a mistake in the prompt, and maybe a reorder point was intended instead.**Calculating EOQ and order cycle** The company operates for 300 days a year, which is important for determining the order cycle length but not for calculating reorder points since we don't have lead time information. I can focus on calculating the EOQ and the number of orders per year. Using the EOQ formula, I compute the EOQ to be approximately 693 units. Then, with the annual demand of 12,000 units divided by EOQ, I find about 17 or 18 orders per year. However, I can't determine slack given the EOQ data.**Determining order frequency and cycle length** Typically, you can have a non-integer number of orders per year, but practically, I’d say the company places about 17 or 18 orders. So, I’ll round it to 17 or 18. For the order cycle length, I can compute that as 300 days divided by 17.31, resulting in approximately 17.33 days between orders. If I find the demand per day, it becomes 40 units. Cycle length would be around 17.32 days using daily demand. Since the lead time isn't given, I won't calculate the reorder point. For part d, I can't compute slack without more details.**Calculating total annual cost at EOQ** To find the total annual cost at EOQ (excluding the purchase cost), I start with the ordering cost, calculated as D/Q multiplied by S. So, it’s 12,000 divided by 692.82, multiplied by $40, resulting in about $692.4. The holding cost is then (Q/2) times H. Dividing 692.82 by 2 and multiplying by 2 gives the same amount. Hence, both costs equal: about $1,385.22 total. I'll round EOQ to 693 units per order, leading to approximately 17 or 18 orders yearly, occurring roughly every 17.3 days.**Finalizing solution calculations** For the cycle length, I calculate T as 300 divided by the number of orders (N), which gives me about 17.32 days. Alternatively, using the EOQ, I get 17.32 days again. So, here's a summary of my findings: a) EOQ ≈ 693 units. b) Number of orders per year ≈ 17.3; order cycle length ≈ 17.3 days. c) There's no information for a reorder point since lead time isn't provided. d) Regarding part d, I note insufficient information; it's not applicable here. I’ll include a step-by-step explanation with this.