**Rocky Mountain Tire Center Inventory Management**Rocky Mountain Tire Center sells 13,000 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 $25 per tire if fewer than 200 tires are ordered, $19 per tire if 200 or more—but fewer than 8,000—tires are ordered, and $15 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).

Given data: Annual demand(D) = 13,000 tiresOrdering cost(S) = $35 per orderHolding Cost (H) = 40% or 0.40 of the purchase price Solution: First, calculate the Holding cost: Quantity Price Holding Cost Q>200 $25 0.4×25 = $10 200-7999 $19 0.4×19 = $7.6 8000 or more $15 0.4×15 = $6 (i) EOQ=2×D×SH Now for EOQ for Q>200 =2×13000×3510 91000 =301.6620626≈302 units This is not feasible as EOQ because not in the quantity range. (ii) (200-7999) =2×13000×357.6 = 119736.8421 =346.0301173≈346 units This is feasible as EOQ because it is in the quantity range. (iii) (8000 or more)=2×13000×356 151666.6667 =389.4440482≈389 units This is not feasible as EOQ because not in the quantity range. Now we are required to compute the Total cost of EOQ = (346) & the total cost of = $15 and Q= 8000 of the Break-even point. Total cost = Q2×H + DQ×S + (Price× Annual Demand) =3462×7.6+13000346×35+19×13000 = 1314.8 + 1315.028902 + 247000= 249629.8289 ≈ $24,9630 Again the total cost of (Q) = (8000) Total cost = Q2×H + DQ×S + (Price× Annual Demand) =8,0002× 6 +13,0008,000×35+15×13,000 =24000 + 56.875+195000=$219056.875≈$219057 Here the total cost of Q= 8000 units is the lowest, thus it is the Optimal order quantity.Q= 8000 units