An office supply company is trying to determine the order quantity for Mt. White fountain pens that are sold to local executives. Annual demand is 5,000 units, and each pen costs the store $50. It costs $75 to place an order, and the inventory carrying cost rate is 30% of item's value. Formulate ONLY the objective function for this problem. Let Q indicate the order quantity. Objective function:
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- Assume the demand for a companys drug Wozac during the current year is 50,000, and assume demand will grow at 5% a year. If the company builds a plant that can produce x units of Wozac per year, it will cost 16x. Each unit of Wozac is sold for 3. Each unit of Wozac produced incurs a variable production cost of 0.20. It costs 0.40 per year to operate a unit of capacity. Determine how large a Wozac plant the company should build to maximize its expected profit over the next 10 years.In Problem 12 of the previous section, suppose that the demand for cars is normally distributed with mean 100 and standard deviation 15. Use @RISK to determine the best order quantityin this case, the one with the largest mean profit. Using the statistics and/or graphs from @RISK, discuss whether this order quantity would be considered best by the car dealer. (The point is that a decision maker can use more than just mean profit in making a decision.)Chris usually sells 120 copies of newspaper each day and believe that sale are normally distributed, with a standard deviation of 15 papers. He pays 70 cents for each paper, which sells $1.25. For each unsold paper, he receives 30-cent credit. a) determine how many papers he should order each day b) calculate the stockout risk for that quantity.
- A golf specialty wholesaler operates 50 weeks per year. Management is trying to determine an inventory policy for its 1-irons, which have the following characteristics:Demand 1D2 = 2,000 units/yearDemand is normally distributedStandard deviation of weekly demand = 3 unitsOrdering cost = $40/orderAnnual holding cost 1H2 = $5/unitsDesired cycle@service level = 90 percentLead time 1L2 = 4 weeksa. If the company uses a periodic review system, what should P and T be? Round P to the nearest week.b. If the company uses a continuous review system, what should R be?An online retailer sells 1,500 t-shirts per year. The cost of the t-shirts to the store is $3.00 and the cost of placing an order is $15 per order. It cost $0.60 per t-shirt per year for the retailer to hold the t-shirts. The retailer sells the t-shirts for $9.99. Determine (a) the optimal order quantity, (b) the order frequency (c) the annual holding and setup cost.13 Pam’s demand for hats is normally distributed with mean 500 and standard deviation 100. She sells her hats for $50 each and buys hats for $10 each, and anything she can't sell by the end of the year, the wholesaler will buy for $5 each. How many hats should she order for next year to maximize profit?
- The materials manager of a tire manfacturer must predict periodically place order for a key chemical one of the raw materials used in manufacturing uses the chemical at a rate of 300lbs each week and the lead time of delivery is 4 days. Assume that the manufacturing operation runs 5 days a week. At what point should the chemical be reorderedd a. when 1200lbs are remaining b. where 0lbs are remaining c. where 375lbs are remaining d. when 240lbs are rem3. Cynthia Knott’s oyster bar buys fresh Louisiana oysters for $5 per pound and sells them for $12 per pound. Any oysters not sold that day are sold to her cousin, who has a nearby grocery store, for $1 per pound. Cynthia believes that demand follows the normal distribution, with a mean of 100 pounds and a standard deviation of 15 pounds. a) What is the cost of underestimating demand for each pound? b) What is the overage cost per pound? c) How many pounds of oyster should she order each day? d) What is the stockout risk for this order size?The reorder point is defined as the lead-time demand for an item. In cases of long lead times, the lead-time demand and thus the reorder point may exceed the economic order quantity Q*. In such cases, the inventory position will not equal the inventory on hand when an order is placed, and the reorder point may be expressed in terms of either the inventory position or the inventory on hand. Consider the economic order quantity model with D = 6,250, C = $40, C₁ = $2, and 250 working days per year. Identify the reorder point in terms of the inventory position and in terms of the inventory on hand for each of the following lead times. (a) 5 days inventory position inventory on hand (b) 15 days inventory position inventory on hand. (c) 25 days inventory position inventory on hand (d) 45 days inventory position inventory on hand
- 39. The home appliance department of a large department store is using a lot size-reorder point system to control the replenishment of a particular model of FM table radio. The store sells an average of 10 radios each week. Weekly demand follows a normal distribution with variance 26. The store pays $20 for each radio, which it sells for $75. Fixed costs of replenishment amount to $28. The accounting department recommends a 20 percent interest rate for the cost of capital. Storage costs amount to 3 percent and breakage to 2 percent of the value of each item. If a customer demands the radio when it is out of stock, the customer will generally go elsewhere. Loss-of-goodwill costs are estimated to be about $25 per radio. Replen- ishment lead time is three months. a. If lot sizes are based on the EOQ formula, what reorder level should be used for the radios? b. Find the optimal values of (Q, R). c. Compare the average annual costs of holding, ordering, and stock-out for the poli- cies that…XYZ’s Hardware is a small family business in Dubai, UAE. The owners, Abdullah and Omar,must use every square foot of store space as profitably as possible. They have never keptdetailed inventory or sales records. As soon as a shipment of goods arrives, the items areimmediately placed on store shelves. Invoices from suppliers are only kept for tax purposes.When an item is sold, the item number and price are rung up at the cash register. The ownersuse their own judgment in identifying items that need to be reordered.a). How could information systems help Abdullah and Omar run their business?b). What data should these systems capture?A health and nutrition store stocks a multivitamin with an annual demand of 1,000 bottles has Co probability distribution with μ = 25 and σ = 5. (a) What is the recommended order quantity? (Round your answer to the nearest integer.) = $23.50 and C = $9. The demand exhibits some variability such that the lead-time demand follows a normal (b) What are the reorder point and safety stock if the store desires at most a 4% probability of stock-out on any given order cycle? (Round your answers to the nearest integer.) reorder point safety stock (c) If a manager sets the reorder point at 30, what is the probability of a stock-out on any given order cycle? (Round your answer to four decimal places.) How many times would you expect a stock-out during the year if this reorder point were used? (Round your answer to the nearest integer.)