Rocky mountain tire center sells 12,000 go cart tires per year. The ordering cos

Question

Rocky mountain tire center sells 12,000 go cart tires per year. The ordering cost for each order is $35, and the holding cost is 40% of the purchase price of the tires per year. The purchase price is $18 per tire if fewer than 200 tires are orderd, $16 per tire if 200 or more are ordered, but fewer than 8,000 tires are ordered, and $13 per tire if 8,000 or more tires are ordered.

A)How manny tires should rocky Mountain order each times it places an order?

Rocky mountains optimal order quantity is ____ units?

B) what is the total cost of this policy?

Total annual cost of ordering optimal order size= $_____

Explanation / Answer

Annual Demand 12000 Ordering Cost $         35.00 Carrying Cost - 40% of price i.e. 40% * $18 $           7.20 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 * 12000 * 35) / 7.2 = 341.565 units or, 382 units This is not feasible solution as qty ordered has to be within 200 units Since supplier gives discount when qty ordered is more than 200, hence EOQ needs to be calculated at each price range Supplier gives disount offer if qty purchased is between 200-8000 units When Price is $16, Carrying cost = $6.40 EOQ = 2AO / C = (2 * 12000 * 35) / 6.40 = 362.2844 or 362 units Supplier gives disount offer if qty purchased is 8000 or more When Price is $13, Carrying cost = $5.2 EOQ = 2AO / C = (2 * 12000 * 35) / 5.2 = 401.9185 or 402 units This is not feasible solution as qty ordered has to be 800 or more. Hence optimal order qty will occur at lowest of range that is 8000 units and for 0-199 units at higher end of range, i.e 199 units Optimal Order Quanity 1 - 199: 199 200 - 7999: 362 8000 or more: 8000 Inventory Order Size (A) 199 362 8000 Price (B) 18.00 16.00 13.00 Direct Cost (Price * Annual Demand = B* 12000) (C) $216,000.00 $192,000.00 $156,000.00 No of orders (Annual Demand/Order Quantity per order = 12000 / A) (D) 60 33 2 Ordering Cost (No orders * $35 = D *$35) ( E) $2,110.55 $1,160.22 $52.50 Carrying Cost per unit (40% * B) (F) $7.20 $6.40 $5.20 Carrying Cost (Order Size / 2 * Carrying Cost per unit per annum = A/2 * F) (G) $716.40 $1,158.40 $20,800.00 Total Cost (B+E+G) $218,826.95 $194,318.62 $176,852.50 Since the total cost is lowest at 8000 units, this is the optimal order quantity. Total Cost of Ordering Optimal Order quanity = $176,852.50

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