Help! Rocky Mountain Tire Centre sells 8,000 go-cart tires per year. The orderin
ID: 448582 • Letter: H
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Rocky Mountain Tire Centre sells 8,000 go-cart tires per year. The ordering cost for each order is $35, and the holding cost is 50% of the purchase price of the tires per year. The purchase price is $22 per tire if fewer than 200 tires are ordered, $16 per tire if 200 or more, but few er than 8,000, tires arc ordered, and $15 per tire if 8,000 or more tires are ordered. How many tires should Rocky Mountain order each time it places an order? Rocky Mountain's optimal order quantity is units (enter your response as a whole number). What is the total cost of this policy? Total annual cost of ordering optimal order size = $ (round your response to the nearest whole number).Explanation / Answer
Annual Demand 8000 Ordering Cost $ 35.00 Carrying Cost - 50% of price ($22) $ 11.00 a. EOQ = 2AO / C where A = Annual Demand O = Ordering Cost per order C = Carrying Cost per unit per annum Initial EOQ at base price EOQ = 2AO / C = (2 * 8000 * 35) / 11 = 225.63 units or, 226 units Since supplier gives discount when qty ordered is more than 200, hence optimal units at this price range is 200 units Supplier gives disount offer if qty purchased is between 200-8000 units, at Price - $16 When Price is $ 16, Carrying cost = $ 8 EOQ = 2AO / C = (2 * 8000 * 35) / 8 = 264.58 units or 265 units Supplier gives disount offer if qty purchased is 8000 units or more. Price - $15 When Price is $ 15, Carrying cost = $ 7.50 EOQ = 2AO / C = (2 * 8000 * 35) / 7.5 = 273.25 units or 273 units This is not feasible solution as qty ordered has to be more than 8000 units. Hence optimal order qty will occur at lowest of range that is 8000 units EOQ - 265 units 0 - 200 - End of range 8000 or more - Beginning of range Inventory Order Size (A) 200 265 8000 Price (B) 22.00 16.00 15.00 Direct Cost (Price * Annual Demand = B*120000) (C) $176,000.00 $128,000.00 $120,000.00 No of orders (Annual Demand/Order Quantity per order = 8000 / A) (D) 40 30 1 Ordering Cost (No orders * $ 35 = D *$35) ( E) $1,400.00 $1,056.60 $35.00 Carrying Cost per unit (50% * B) (F) 11.00 8.00 7.50 Carrying Cost (Order Size / 2 * Carrying Cost per unit per annum = A/2 * F) (G) $1,100.00 $1,060.00 $30,000.00 Total Cost (B+E+G) $178,500.00 $130,116.60 $150,035.00 Since the total cost is lowest at 265 units, this is the optimal order quantity. Total Cost of Ordering Optimal Order quanity = $ 130,116.60
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