Kenichi Kaneko is the manager of a production department which uses 400 boxes of rivets per year. To hold down his inventory level, Kenichi has been ordering only 50 boxes each time. However, the supplier of rivets now is offering a discount for higher-quantity orders according to the following price schedule, where the price for each category applies to every box purchased.

The company uses an annual holding cost rate of 20 percent of the price of the item. The total cost associated with placing an order is $80 per order. Kenichi has decided to use the EOQ model with quantity discounts to determine his optimal inventory policy for rivets.

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(a) For each discount category, write an expression for the total cost per year (TC) as a function of the order quantity Q.

T (b) For each discount category, use the EOQ formula for the basic EOQ model to calculate the value of Q (feasible or infeasible) that gives the minimum value of TC. (You may use the analytical version of the Excel template for the basic EOQ model to perform this calculation if you wish.)

(c) For each discount category, use the results from parts (a) and (b) to determine the feasible value of Q that gives the feasible minimum value of TC and to calculate this value of TC.

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