2. Zara is determining how many coats to order for this upcoming winter selling season. Zara forecasts the demand distribution for coats this upcoming winter to be the following. Demand (number of coats) Probability 100 0.2 150 0.1 200 0.2 250 0.1 300 350 0.1 0.3 Each coat costs Zara $100 to purchase wholesale and sells for $200 retail. At the end of the winter selling season, Zara may sell as many coats as it desires at a salvage value of $50 per coat. a. Suppose that Zara has purchased 250 coats, what is the marginal value from a 251st coat? Is it profitable for Zara to purchase its 251st coat? Justify your answer. b. Suppose that Zara has purchased 260 coats, what is the marginal value from a 261st coat? Is it profitable for Zara to purchase its 261st coat? Justify your answer. c. What is the optimal number of coats for Zara to purchase in order to maximize its average profit?
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- The Pigskin Company produces footballs. Pigskin must decide how many footballs to produce each month. The company has decided to use a six-month planning horizon. The forecasted monthly demands for the next six months are 10,000, 15,000, 30,000, 35,000, 25,000, and 10,000. Pigskin wants to meet these demands on time, knowing that it currently has 5000 footballs in inventory and that it can use a given months production to help meet the demand for that month. (For simplicity, we assume that production occurs during the month, and demand occurs at the end of the month.) During each month there is enough production capacity to produce up to 30,000 footballs, and there is enough storage capacity to store up to 10,000 footballs at the end of the month, after demand has occurred. The forecasted production costs per football for the next six months are 12.50, 12.55, 12.70, 12.80, 12.85, and 12.95, respectively. The holding cost incurred per football held in inventory at the end of any month is 5% of the production cost for that month. (This cost includes the cost of storage and also the cost of money tied up in inventory.) The selling price for footballs is not considered relevant to the production decision because Pigskin will satisfy all customer demand exactly when it occursat whatever the selling price is. Therefore. Pigskin wants to determine the production schedule that minimizes the total production and holding costs. As indicated by the algebraic formulation of the Pigskin model, there is no real need to calculate inventory on hand after production and constrain it to be greater than or equal to demand. An alternative is to calculate ending inventory directly and constrain it to be nonnegative. Modify the current spreadsheet model to do this. (Delete rows 16 and 17, and calculate ending inventory appropriately. Then add an explicit non-negativity constraint on ending inventory.)The Pigskin Company produces footballs. Pigskin must decide how many footballs to produce each month. The company has decided to use a six-month planning horizon. The forecasted monthly demands for the next six months are 10,000, 15,000, 30,000, 35,000, 25,000, and 10,000. Pigskin wants to meet these demands on time, knowing that it currently has 5000 footballs in inventory and that it can use a given months production to help meet the demand for that month. (For simplicity, we assume that production occurs during the month, and demand occurs at the end of the month.) During each month there is enough production capacity to produce up to 30,000 footballs, and there is enough storage capacity to store up to 10,000 footballs at the end of the month, after demand has occurred. The forecasted production costs per football for the next six months are 12.50, 12.55, 12.70, 12.80, 12.85, and 12.95, respectively. The holding cost incurred per football held in inventory at the end of any month is 5% of the production cost for that month. (This cost includes the cost of storage and also the cost of money tied up in inventory.) The selling price for footballs is not considered relevant to the production decision because Pigskin will satisfy all customer demand exactly when it occursat whatever the selling price is. Therefore. Pigskin wants to determine the production schedule that minimizes the total production and holding costs. Modify the Pigskin model so that there are eight months in the planning horizon. You can make up reasonable values for any extra required data. Dont forget to modify range names. Then modify the model again so that there are only four months in the planning horizon. Do either of these modifications change the optima] production quantity in month 1?Lemingtons is trying to determine how many Jean Hudson dresses to order for the spring season. Demand for the dresses is assumed to follow a normal distribution with mean 400 and standard deviation 100. The contract between Jean Hudson and Lemingtons works as follows. At the beginning of the season, Lemingtons reserves x units of capacity. Lemingtons must take delivery for at least 0.8x dresses and can, if desired, take delivery on up to x dresses. Each dress sells for 160 and Hudson charges 50 per dress. If Lemingtons does not take delivery on all x dresses, it owes Hudson a 5 penalty for each unit of reserved capacity that is unused. For example, if Lemingtons orders 450 dresses and demand is for 400 dresses, Lemingtons will receive 400 dresses and owe Jean 400(50) + 50(5). How many units of capacity should Lemingtons reserve to maximize its expected profit?
- 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.If a monopolist produces q units, she can charge 400 4q dollars per unit. The variable cost is 60 per unit. a. How can the monopolist maximize her profit? b. If the monopolist must pay a sales tax of 5% of the selling price per unit, will she increase or decrease production (relative to the situation with no sales tax)? c. Continuing part b, use SolverTable to see how a change in the sales tax affects the optimal solution. Let the sales tax vary from 0% to 8% in increments of 0.5%.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.)
- If the number of competitors in Example 11.1 doubles, how does the optimal bid change?3-2) The optimal quantity of the three products and resulting revenue for Taco Loco is: A) 28 beef, 80 cheese, and 39.27 beans for $147.27. B) 10.22 beef, 5.33 cheese, and 28.73 beans for $147.27. C) 1.45 Z, 8.36 Y, and 0 Z for $129.09. D) 14 Z, 13 Y, and 17 X for $9.81. 3-3) Taco Loco is unsure whether the amount of beef that their computer thinks is in inventory is correct. What is the range in values for beef inventory that would not affect the optimal product mix? A) 26 to 38.22 pounds B) 27.55 to 28.45 pounds C) 17.78 to 30 pounds D) 12.22 to 28 poundsSuppose a grocer is faced with a problem of how many cases of milk to stock to meet this week’s demand. The grocer estimates that 10, 15, 20, or 25 cases will be needed and wants to analyze the situation using a payoff table and decision theory to determine how many cases to stock. Every case of milk costs the grocer $55 and will be sold for $90 (if sold during the week). If there are cases left at the end of the week, they will be sold to a food bank for $30 per case. Fill in the payoff table (Using Excel - calculate the payoff for each combination of cases of milk ordered and cases of milk demanded). Cases demanded 10 15 20 25 Cases stocked 10 15 20 25 B. Assume the probability of demand is determined as in the table below. Demand 10 cases 15 cases 20 cases 25 cases Probability .08 .25 .45 .22 Calculate the Expected…
- PROBLEM The Seminole Company wishes to apply the Miller-Orr model to manage its cash investment. Seminole’s management has determined that the cost of either investing in or selling marketable securities is $200. By looking at Seminole Company’s past cash needs, they have determined that the variance of daily cash flows is $10,000. Seminole Company’s opportunity cost of cash, per day, is estimated to be 0.05%. Seminole management has figured, based on their experience dealing with the cash flows of the company, that there should be a cushion— a safety stock—of cash of $20,000. 1. How much is the variance of daily cash flows? (Use a number, no decimal value, no commas, no currency, no space) * 2. How much is the opportunity cost of cash, per day? (Use a number, must be in decimal form. eg. 6.3%/100, encode 0.063 , no commas, no currency, no space) * 3. How much is the cost per transaction? (Use a number, no decimal value, no commas, no currency, no space) * PLEASE ANSWER ALL QUESTIONS.…Bob and Dora Sweet wish to start investing $1,000 each month. The Sweets are looking at five investment plans and wish to maximize their expected return each month. Assume interest rates remain fixed and once their investment plan is selected they do not change their mind. The investment plans offered are: Fidelity 9.1% return per year Optima 16.1% return per year CaseWay 7.3% return per year Safeway 5.6% return per year National 12.3% return per year Since Optima and National are riskier, the Sweets want a limit of 30% per month of their total investments placed in these two investments. Since Safeway and Fidelity are low risk, they want at least 40% of their investment total placed in these investments.Formulate the LP model for this problem, using the standard LP format. Remember to define the objective function, the decision variables, and label the constraint functions. There is no need to solve the problem. Note:- Do not provide handwritten solution. Maintain…The produce manager at the local Pig & Whistle grocery store must determine how many pounds of bananas to order weekly. Based upon past experience, the demand for bananas is expected to be 100, 150, 200, or 250 pounds with the following probabilities: 100lbs 0.20; 150lbs 0.25, 200lbs 0.35, 250lbs 0.20. The bananas cost the store $.45 per pound and are sold for $.85 per pound. Any unsold bananas at the end of each week are sold to a local zoo for $.30 per pound. Use your knowledge of decision analysis to model and solve this problem in order to recommend how many pounds of bananas the manager should order each week