Question

Rocky Mountain Tire Center sells 9,000 ​go-cart tires per year. The ordering cost for each order is ​$35​, and the holding cost is 30​% of the purchase price of the tires per year. The purchase price is ​$21 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 ​$13 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 is ...... units ​(enter your response as a whole​ number).

Answer 1

Using given data: Annual demand (o)= 9000 Order cost (o)= $35 Holding cost (H) = 0.3 x Unit Price Economic order Quantity (0) 2XDXO H QC - 200 Taking at Unit Price = $21 * * 2x 9000x 35 = 316.2 6.3x21 - Its out of range Taking * Q2 Reject 200 cac EQc8000 at Unit Price = $18 2x 9000x 35 = 341.5 341 u 0.3x18 Its within ra range Accept Now, Total cost = pxot QXH + DX Unit Price (TC) 9000x35+34) X0-3X18 + 9000x 18 $163844.45 Q -TC₂= 341 -

"Now, For Unit Price = $13 for Q28000 2x9000x35 401:9 3 0.3713 401.9 <8000 Take Q2 = 8000 & find TC3 :- Thai 9000x35+ 8000 x0.3x13 + 9000x13 8000 $127439.37 2 -> Since TCgc LTC2 = 8000 units a) = Optimal order Quantity