Thomas Peterson, general manager for Topp Desk Company, is exasperated because the company exhausted its finished goods

Question:

Thomas Peterson, general manager for Topp Desk Company, is exasperated because the company exhausted its finished goods inventory of Style 103-Modern Desk twice during the previous month. This led to customer complaints and disrupted the normal flow of operations.
"We ought to be able to plan better," declared Peterson during a presentation of his findings to management. "Our annual sales demand is 18,000 units for this model or an average of 75 desks per day based upon our 240-day work year. Unfortunately, the sales pattern is not this uniform. Our daily demand for that model varies considerably. If we do not have the units on hand when a customer places an order, 35% of the time we lose the sale, 40% of the time we pay an extra charge of $24 per unit to expedite shipping when the unit becomes available, and 25% of the time the customer accepts a back order at no out-of-pocket cost to us. A lost sale reduces the contribution to profit by $60."
Peterson displayed the following chart, showing the weighted average (sometimes called expected value) cost of a stock out on a given day.
75 desks per day x $60 x 35% .....................................$1,575
75 desks per day x $24 x 40% ..................................... 720
Back order (no out-of-pocket cost) x 25% ....................... 0
Stock out cost ........................................................$2,295
"When we run out of units," he continued, "we cannot convert the production line immediately, because we disrupt the production of our other products and cause cost increases. The setup process for this model on any stock out day inevitably results in the destruction of 12 finished desks, leaving no salvageable materials. Once we get the line up, we can produce 200 units per day. I would prefer to have several planned runs of a predetermined, uniform quantity rather than the short unplanned runs we have often used to meet unfilled customer orders."
The manager of the Cost Accounting Department suggested that they use an EOQ model to determine optimum production runs and then establish a safety stock to guard against stock outs. The cost data for the Modern Desk that sells for $110 are taken from the accounting records as follows:

The Cost Accounting Department estimates that the company's carrying costs are 19.2% of the incremental out-of-pocket manufacturing costs. This percentage can be broken down into a 10.8% variable rate and an 8.4% fixed rate.
Required:
(1) Topp Desk Company believes that it can solve part of its production scheduling problems by adapting the EOQ model to determine the optimum production run.
(a) Explain what costs the company will be attempting to minimize when it adapts the EOQ model to production runs.
(b) Using the EOQ model, calculate the optimum quantity that Topp Desk Company should manufacture in each production run of Style 103-Modern Desk.
(c) Calculate the number of production runs of Modern Desks that Topp Desk Company should schedule during the year based on the optimum quantity calculated in requirement lb.
(2) Topp Desk Company should establish a safety stock level to guard against stock outs.
(a) Explain the factors that affect the desired size of the safety stock for any inventory item.
(b) Calculate the minimum safety stock level that Topp Desk Company could afford to maintain for Style 103-Modern Desk and not be worse off that it is when it is unable to fill orders equal to an average day's demand.