$2.$ BASIC EPQ QUESTION: A company is about to begin production of a new product. The manager of the department that will produce one of the components for the product wants to know how often the machine used to produce the item will be available for other work. The machine will produce the item at a rate of $80$ units a day. Sixty units will be used daily in assembling the final product. Assembly will take place five days a week, $50$ weeks a year. The manager estimates that it will take almost a full day to get the machine ready for a production run, at a cost of $$200.$ Inventory holding costs will be $$10$ per year. REQUIRED: a$.$ What run quantity $($EPQ$)$ should be used to minimize total annual costs? b What is the length of a production run in days? c$.$ What is the cycle time? d What would the average inventory be for this lot size? e About how many runs per year would there be$?$ f If the manager wants to run another job between runs of this item, and needs a minimum of $10$ days per cycle for the other work, will there be enough time? g During production, at what rate will inventory build up$?$