Problem 2 Kenichi Kaneko is the manager of a production department which uses 10,000 boxes of rivets per year. To hold down his inventory level, Kenichi has been ordering only 500 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. discount category 1 2 3 4 quantity 1 to 999 1000 to 1499 1500 to 1999 2000 and over Price (per box) $ 8.50 $ 8.00 7.50 $ $ 7.00 The company uses an annual holding cost rate of 25 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. (a) For each discount category, use the EOQ formula to calculate the value of Q that gives the minimum value of TC. (b) For each discount category, determine the feasible value of Q that gives the feasible minimum value of TC, and calculate this value of TC. (c) Graph the curves of TC versus Q for each of the four discount categories, changing Q from Q=500 to Q=2,200 in increments of 50. Then, use a solid line to emphasize the feasible region of TC for all possible values of Q. Show the breakpoints identified in (b) (d) Determine the optimal order quantity and the corresponding value of TCmin (total cost/year). (e) Given the optimal order quantity from part (d), what is the time interval between orders, in working days? Assume the company works 250 days per year (f) What would be the % of reduction in TC by switching from current practice to the optimal policy recommended in (d)

Problem 2 Kenichi Kaneko is the manager of a production department which uses 10,000 boxes of rivets per year. To hold down his inventory level, Kenichi has been ordering only 500 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 25 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. (a) For each discount category, use the EOQ formula to calculate the value of Q that gives the minimum value of TC. (b) For each discount category, determine the feasible value of Q that gives the feasible minimum value of TC, and calculate this value of TC. (c) Graph the curves of TC versus Q for each of the four discount categories, changing Q from Q=500 to Q=2,200 in increments of 50 . Then, use a solid line to emphasize the feasible region of TC for all possible values of Q. Show the breakpoints identified in (b) (d) Determine the optimal order quantity and the corresponding value of TCmin (total costlyear) (e) Given the optimal order quantity from part (d), what is the time interval between orders, in working days? Assume the company works 250 days per year (f) What would be the \% of reduction in TC by switching from current practice to the optimal policy recommended in (d)