Please answer both questions. Rocky Mountain Tire Center sells 10,000 go-cart ti
ID: 435326 • Letter: P
Question
Please answer both questions.
Rocky Mountain Tire Center sells 10,000 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 $19 per tire if fewer than 200 tires are ordered, $18 per tire if 200 or more, but fewer than 8,000, tires are ordered, and $17 per tire if 8,000 or more tires are ordered a) How many tires should Rocky Mountain order each time it places an order? Rocky Mountain's optimal order quantity isunits (enter your response as a whole number).Explanation / Answer
Rocky mountain tire center
Annual Demand =10000 per year
Ordering cost = 35 per order
Holding cost = 50% of cost of item
Order quantity
Cost per item
200 or less
$19
200 to 7999
$18
8000 or more
$17
EOQ = SQRT(2*annual demand* ordering cost / holding cost)
EOQ(200 or less) = SQRT( ( 2*10000* 35) / (0.5*19) ) =271.45
EOQ(200 to 7999) = SQRT( ( 2*10000* 35) / (0.5*18) ) =278.89
EOQ(8000 or more) = SQRT( ( 2*10000* 35) / (0.5*17) ) =286.97
Order quantity
Cost per item
EOQ(rounded)
Remark
1 to199
$19
272
Feasible
200 to 7999
$18
279
Feasible
8000 or more
$17
287
Infeasible
*Infeasible – We cannot get a discounted price of $17 at an order quantity of 287. We need to order minimum 8000.Also note that in first case (1-199), we can order 272 at $19, though this order quantity is eligible for discount
Total annual cost
= Purchase cost+ Inventory cost
= purchase cost+ ordering cost+ carrying cost
= p*d+ O * d/Q + c * Q/2
Total cost ( Q=272)= 19*10000 + 35 * (10000/272) + (0.5*19) * (272/2) =192578.77
Total cost ( Q=279)= 18*10000 + 35 * (10000/279) + (0.5*18)* (279/2) =182509.98(<- cheapest)
Total cost ( Q=8000)= 17*10000 + 35 * (10000/8000) + (0.5*17) * (8000/2) = 204043.75
Hence Optimal order quantity is 279 units with total cost = $182509.98
Order quantity
Cost per item
200 or less
$19
200 to 7999
$18
8000 or more
$17