A manufacturing company receives orders for vehicle audio systems from two assembly plants in Atlanta and Little Rock. Atlanta needs at least 45 audio systems and Little Rock needs at least 32 audio systems. The company can send at most 139 audio systems to these assemply plants. It costs $34 per system to ship to Atlanta and $50 per system to ship to Little Rock. Atlanta gives the manufacturing company $20 in rebates toward its products for each audio system they buy, while Little Rock gives $15 in rebates. The manufacturer estimates they need at least $1500 in rebates to cover products they plan to buy from the two plants. How many audio systems should be shipped to each plant to minimize shipping costs. What is the minimum cost? Number of audio systems to ship to Atlanta: Number of audio systems to ship to Little Rock: Minimum cost: $
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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.The Tinkan Company produces one-pound cans for the Canadian salmon industry. Each year the salmon spawn during a 24-hour period and must be canned immediately. Tinkan has the following agreement with the salmon industry. The company can deliver as many cans as it chooses. Then the salmon are caught. For each can by which Tinkan falls short of the salmon industrys needs, the company pays the industry a 2 penalty. Cans cost Tinkan 1 to produce and are sold by Tinkan for 2 per can. If any cans are left over, they are returned to Tinkan and the company reimburses the industry 2 for each extra can. These extra cans are put in storage for next year. Each year a can is held in storage, a carrying cost equal to 20% of the cans production cost is incurred. It is well known that the number of salmon harvested during a year is strongly related to the number of salmon harvested the previous year. In fact, using past data, Tinkan estimates that the harvest size in year t, Ht (measured in the number of cans required), is related to the harvest size in the previous year, Ht1, by the equation Ht = Ht1et where et is normally distributed with mean 1.02 and standard deviation 0.10. Tinkan plans to use the following production strategy. For some value of x, it produces enough cans at the beginning of year t to bring its inventory up to x+Ht, where Ht is the predicted harvest size in year t. Then it delivers these cans to the salmon industry. For example, if it uses x = 100,000, the predicted harvest size is 500,000 cans, and 80,000 cans are already in inventory, then Tinkan produces and delivers 520,000 cans. Given that the harvest size for the previous year was 550,000 cans, use simulation to help Tinkan develop a production strategy that maximizes its expected profit over the next 20 years. Assume that the company begins year 1 with an initial inventory of 300,000 cans.The Fish House (TFH) in Norfolk, Virginia, sells fresh fish and seafood. TFH receives daily shipments of farm-raised trout from a nearby supplier. Each trout costs $2.45 and is sold for $3.95. To maintain its reputation for freshness, at the end of the day TFH sells any leftover trout to a local pet food manufacturer for $1.25 each. The owner of TFH wants to determine how many trout to order each day. Historically, the daily demand for trout is: Demand 10 11 12 13 14 15 16 17 18 19 20 Probability 0.02 0.06 0.09 0.11 0.13 0.15 0.18 0.11 0.07 0.05 0.03 a. Construct a payoff matrix for this problem. b. How much should the owner of TFH be willing to pay to obtain a demand forecast that is 100% accurate? give a clear explanation for (b)
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- Arts N Crafts Industries manufacturers high-end light fixtures, which it sells internationally. The company is responsible for paying for shipping its product to a distributor located in Atlanta, Georgia. Due to the high cost of shipping, the company is considering shipping its products unassembled, but will include detailed assembly instructions in each package. By shipping unassembled products, Arts N Crafts will be able to shrink the size of its cartons and thereby increase the number of products per pallet from 16 (4 rows of 4) to 25 (5 rows of 5). Note that this change will not appreciably increase each product’s 8-pound shipping weight. Furthermore, since individual fixtures will be packed more tightly, they will be less susceptible to damage and easier to handle. Thus, the company expects the freight class to decrease from 85 to 70. Currently the company ships 400 units per week.a. Using Table, assess the impact of the proposed change in packaging on weekly shipping cost.b. How…. A refiner in city Q serves four customers near city W and maintains consignment inventory (owned by the refiner) at each location. Currently, the refiner uses TL (truckload) transportation to deliver separately to each customer. Each truck costs $(759) plus $(309) per stop. The refiner is considering aggregating deliveries to city W on a single truck. The demand of the first customer is 75 tons a year, the demand of the second customer is 30 tons per year, and the demand of the third and fourth customers is 10 tons per year. The product cost is $8,000 per ton, and it uses a holding cost of (24)%. The truck capacity is 20 tons. a. What is the optimal delivery policy to each customer if the refiner ships separately to each of them? What is the annual total inventory-related cost? b. What is the optimal delivery policy to each customer if the refiner aggregates shipments to each of the four customers on every truck that goes to city W? What is the annual total inventory-related cost?…Osmanli Solutions (Pvt) Ltd is a leading software house of Istanbul and has recently opened its development center in Karachi and has hired you as the General Manager of the Karachi division. The top executives at the headquarters of Osmanli Solutions (Pvt) Ltd feel that they have surplus workforce at their Istanbul office and therefore wants to transfer the surplus workforce to Karachi office in order to reduce the operational cost of their Istanbul office. Under these circumstances, you found yourself in a position that 30% of the entire workforce at Karachi office will consists of those employees who are to be transferred from the Istanbul office. What will be your concerns as the leader of the Karachi unit under these circumstances. Q 2 How will you deal with the situation?
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