Complete the model.Mins.t.+ 50.Q₁, Q₂ Q3 ≥ 0.Q₂2,000 +Q3Total cost = $+- 1,000 +.Q₁ +Q₁Q₂Q32,000)2,000)- 1,000)Q₂ ++0.30.+0.30.+0.30.Q3 € 9,000).9/1Solve the model. (Round Q₁, Q₂, and Q₂ to three decimal places and total cost (in $) to two decimal places.)Q₂ON The economic order quantity (EOQ) model is a classical model used for controlling inventory and satisfying demand. Costs included in the model are holding cost per unit, ordering cost, and the cost of goods ordered. The assumptions for that model are that only a single item is considered, that theentire quantity ordered arrives at one time, that the demand for the item is constant over time, and that no shortages are allowed.Suppose we relax the first assumption and allow for multiple items that are independent except for a restriction on the amount of space available to store the products. The following model describes this situation.Let= annual demand for item j= unit cost of item jS₁ = cost per order placed for item jW, = space required for item jW = the maximum amount of space available for all goods¡ = inventory carrying charge as a percentage of the cost per unit.The decision variables are Q₁, the amount of item j to order. The model is$ [50, +501 +10,21]j=1NMinimizes.t.j = 1w;Q; swQ, ≥ 0.In the objective function, the first term is the annual cost of goods, the second is the annual ordering cost (D/Q, is the number of orders), and the last term is the annual inventory holding cost (Q/2 is the average amount of inventory).Construct and solve a nonlinear optimization model for the following data.i = 0.30Annual DemandItem Cost ($)Order Cost ($)Space Required (sq. feet)W = 9,000Item 1 Item 2 Item 32,000100150502,00050135251,0008012540

Non-linear programming model involves finding an optimal solution when relationships between the…

Answered: Complete the model. Min s.t. + 50 Q₁ Q₂…

Practical Management Science

6th Edition

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Publisher:WINSTON, Wayne L.

Chapter2: Introduction To Spreadsheet Modeling

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Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...

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Suppose the following item is being managed using a fixed-order quantity model with safety stock. Annual Demand = 100,000 units Order quantity = 30,000 units Safety stock = 4000 units What are the average inventory level and inventory turnover for this item?
Company ABC utilizes an inventory system in which order gets placed after uniform time duration. Which of the following represents the inventory policy used by the Company? a) (0, x) Model b) EOQ Model c) Fixed period model d) Fixed quantity model
6-23 Barbara Bright is the purchasing agent for West Valve Company. West Valve sells industrial valves and fluid control devices. One of the most popular valves is the Western, which has an annual demand of 4,000 units. The cost of each valve is $90, and the inventory carrying cost is estimated to be 10% of the cost of each valve. Barbara has made a study of the costs involved in placing an order for any of the valves that West Valve stocks, and she has concluded that the average ordering cost is $25 per order. Furthermore, it takes about two weeks for an order to arrive from the supplier, and during this time, the demand per week for West valves is approximately 80. d. What is the average inventory? What is the annual holding cost? e. How many orders per year would be placed? What is the annual ordering cost?
6-23 Barbara Bright is the purchasing agent for West Valve Company. West Valve sells industrial valves and fluid control devices. One of the most popular valves is the Western, which has an annual demand of 4,000 units. The cost of each valve is $90, and the inventory carrying cost is estimated to be 10% of the cost of each valve. Barbara has made a study of the costs involved in placing an order for any of the valves that West Valve stocks, and she has concluded that the average ordering cost is $25 per order. Furthermore, it takes about two weeks for an order to arrive from the supplier, and during this time, the demand per week for West valves is approximately 80. a. What is the EOQ? b. What is the ROP? c. Is the ROP greater than the EOQ? If so, how is this situation handled? d. What is the average inventory? What is the annual holding cost? e. How many orders per year would be placed? What is the annual ordering cost?
A manufacturer of exercise equipment purchases the pulley section of the equipment from a supplier who lists these prices: Less than 1000 $5.00 each 1000 to 3999 $4.95 each 4000 to 5999 $4.90 each 6000 or more $4.85 each Ordering costs are $50, annual carrying costs per unit are 40 percent of purchase cost, and annual usage is 4900 pulleys. Determine the order quantity that will minimize total cost.
In a periodic order system, the lead time for a box of weed killer is 2 weeks. The review period is 1 week. Demand during the protection interval (i.e. review period +lead time) averages 218 boxes, with a standard deviation of 40 boxes. a.) What is the cycle-service level when the target inventory is set at 300 boxes? b.) In the fall season, demand for weed killer decreases but also becomes more variable. Assume demand during the protection interval is expected to decrease to 180 boxes, but with a standard deviation of 50 boxes. What would be the cycle-service level if management keeps the target inventory level set at 300 boxes? C) if the solution is feasible, should the order quantity change
The TransCanada Lumber Company and Mill processes10,000 logs annually, operating 250 days per year. Immediately upon receiving an order, the logging company’ssupplier begins delivery to the lumber mill at the rate of 60logs per day. The lumber mill has determined that the ordering cost is $1600 per order, and the cost of carrying logsin inventory before they are processed is $15 per log on anannual basis. Determine the following:a. The optimal order sizeb. The total inventory cost associated with the optimalorder quantityc. The number of operating days between ordersd. The number of operating days required to receive anorde
Among the following multi-period inventory models, which one has the highest probability of stockout? A. Fixed Order Quantity with Safety Stock B. Fixed Time Period Model C. Fixed Order Quantity D. Both Fixed Order Quantity & Fixed Order Quantity with Safety Stock
An item has normally distributed demand with a mean of 100 and a standard deviation of 50. They order a week with one week lead time. Backorders are allowed. A) With an order-up-to level of 300, on-hand inventory of 200, and on-order inventory of 60, how much will be ordered this week? B) What is the standard deviation of demand over 2 weeks?
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The annual demand for an automobile component is 50,000 units. The carrying cost is Rs. 60/unit/year, the ordering cost is Rs. 200.00/order, and the shortage cost is Rs. 110.00/unit/year. Find the optimal values of the following: (a) Economic order quantity (b) Maximum inventory (c) Maximum shortage quantity (d) Cycle time (e) Inventory period (t1) (f) Shortage period (t2).
Catlea Merchandising is engaged in selling school shoesfor both boys and girls in their teenage years. Catlea needs 32,000 pairs of shoes in a year in order to satisfy the market demand. It costs ₱ 48 to place an order while ₱ 8 is needed to hold each quantity of shoe in Catlea's inventory. Upon checking on Catlea's supplier, it takes 8 days in between placing an order and eventually receiving it. a. Determine the Economic Order Quantityb. Determine the number of order per monthc. Determine the reorder point

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Complete the model. Min s.t. + 50 Q₁ Q₂ Q3 ≥ 0. 2,000 + + 1,000 + • Q₁ + Q₁ Q₂ 2,000 2,000 - 1,000 Q₂ + + 0.30. + 0.30. ON Li + 0.30. . Q3 ≤ 9,000 4 Solve the model. (Round Q₁, Q₂, and Q₂ to three decimal places and total cost (in $) to two decimal places.)