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Discuss the process of Refining Alphas, and why this process is a good alternative to constrained optimization.
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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.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?It costs a pharmaceutical company 75,000 to produce a 1000-pound batch of a drug. The average yield from a batch is unknown but the best case is 90% yield (that is, 900 pounds of good drug will be produced), the most likely case is 85% yield, and the worst case is 70% yield. The annual demand for the drug is unknown, with the best case being 20,000 pounds, the most likely case 17,500 pounds, and the worst case 10,000 pounds. The drug sells for 125 per pound and leftover amounts of the drug can be sold for 30 per pound. To maximize annual expected profit, how many batches of the drug should the company produce? You can assume that it will produce the batches only once, before demand for the drug is known.
- Elaborate/ Explain Integer Linear Optimization and put examplesExplain the term “Constrained Optimization” as Thaler used in the first chapter of Misbehaving.In the past, Peter Kelle's tire dealership in Baton Rouge sold an average of 1,000 radials each year. In the past 2 years, 240 and 240, respectively were sold in fall, 350 and 320 in winter,150 and165 in spring, and 340 and 195 in summer. With a major expansion planned, Kelle projects sales next year to increase to 1,200 radials. Based on next year's projected sales, the demand for each season is going to be (enter your responses as whole numbers): Fall: Winter: Spring: Summer:
- How do non-linear system models differ from linear models, and what are the challenges associated with analyzing and controlling them?Millie wants to install a new carpet in the living room of her house. She calculated the square footage of the room and then multiplied it by a set cost factor to estimate the cost. This is an example of_________ Group of answer choices Parametric estimating Three-point estimating Bottom-up estimating Analogous estimatingWhat combination of x and y will yield the optimum for this problem? Maximize Z = $3x + $15y Subject to: Multiple Choice x= 0, y=4 x= 0, y=3 x= 0, y=0 x= 2y=0 O x=1,y=25 2x + 4y ≤ 12 5x + 2y ≤ 10
- Round Tree Manor is a hotel that provides two types of rooms with three rental classes: Super Saver, Deluxe, and Business. The profit per night for each type of room and rental class is as follows: Rental Class Super Saver Deluxe Business Room Type I $30 $35 — Type II $20 $30 $40 Type I rooms do not have high-speed Internet access and are not available for the Business rental class. Round Tree's management makes a forecast of the demand by rental class for each night in the future. A linear programming model developed to maximize profit is used to determine how many reservations to accept for each rental class. The demand forecast for a particular night is 160 rentals in the Super Saver class, 50 rentals in the Deluxe class, and 40 rentals in the Business class. Round Tree has 100 Type I rooms and 120 Type II rooms. 1. **Use linear programming to determine how many reservations to accept in each rental class and how the…In the past, Peter Kelle's tire dealership in Baton Rouge sold an average of 1,000 radials each year. In the past 2 years, 220 and 250, respectively were sold in fall, 360 and 320 in winter, 145 and 175 in spring, and 300 and 230 in summer. With a major expansion planned, Kelle projects sales next year to increase to 1,200 radials. Based on next year's projected sales, the demand for each season is going to be (enter your responses as whole numbers): Season Demand Fall nothingThe monthly forecasts for Gravity Room Furniture Ltd. (GRF), a manufacturer of outdoor furniture, is shown in the table below. The factory is open for 6 hrs/day and 25 days/month. To produce one unit, an employee needs 30 hrs of labor, and gets paid $5/hr for regular time and $6/hr for overtime, with a maximum of 20 hrs of overtime per month (per employee). The materials needed to make a unit cost $50. GRF can hire and train a new employee for $500 and lay off one for $400. Inventory costs $3 per unit on hand at the end of each month. At present, 140 employees are on the payroll, anticipated starting inventory is 100 units, and GRF would like to end the year with the same level of inventory. Month Demand Jan 300 Feb 300 Mar 500 Apr 500 May 700 June 900 July 1300 Aug 1600 Sept 900 Oct 500 Nov 300 Dec 300 A. what is the stockout cost? B. What is the subcontractor cost? C. A third party has offered to produce the furniture as needed at a cost of $230 per unit…