solve the system of linear equation 0.02x1-0.05x2= -0.19 0.03x1+0.04x2=0.52 X1= X2=-0.04 No solution O X1=8 X2=7
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- Cholesterol Cholesterol in human blood is necessary, but too much can lead to health problems. There are three main types of cholesterol: HDL (high-density lipoproteins), LDL (low-density lipoproteins), and VLDL (very low-density lipoproteins). HDL is considered “good” cholesterol; LDL and VLDL are considered “bad” cholesterol. A standard fasting cholesterol blood test measures total cholesterol, HDL cholesterol, and triglycerides. These numbers are used to estimate LDL and VLDL, which are difficult to measure directly. Your doctor recommends that your combined LDL/VLDL cholesterol level be less than 130 milligrams per deciliter, your HDL cholesterol level be at least 60 milligrams per deciliter, and your total cholesterol level be no more than 200 milligrams per deciliter. (a) Write a system of linear inequalities for the recommended cholesterol levels. Let x represent the HDL cholesterol level, and let y represent the combined LDL VLDL cholesterol level. (b) Graph the system of inequalities from part (a). Label any vertices of the solution region. (c) Is the following set of cholesterol levels within the recommendations? Explain. LDL/VLDL: 120 milligrams per deciliter HDL: 90 milligrams per deciliter Total: 210 milligrams per deciliter (d) Give an example of cholesterol levels in which the LDL/VLDL cholesterol level is too high but the HDL cholesterol level is acceptable. (e) Another recommendation is that the ratio of total cholesterol to HDL cholesterol be less than 4 (that is, less than 4 to 1). Identify a point in the solution region from part (b) that meets this recommendation, and explain why it meets the recommendation.In recent years major efforts have been made to standardize accounting practices in different countries; this is called harmonization. In an article in Accounting and Business Research, Emmanuel N. Emenyonu and Sidney J. Gray studied the extent to which accounting practices in France, Germany, and the U.K. are harmonized. (a) Depreciation method is one of the accounting practices studied by Emenyonu and Gray. Three methods were considered—the straight-line method (S), the declining balance method (D), and a combination of D & S (sometimes European firms start with the declining balance method and then switch over to the straight-line method when the figure derived from straight line exceeds that from declining balance). The data in the table (below) summarize the depreciation methods used by a sample of 78 French, German, and U.K. firms. Depreciation Methods France Germany UK Total A. Straight line (S) 15 0 25 40 B. Declining Bal (D) 1 1 1 3 C. (D & S) 10…In recent years major efforts have been made to standardize accounting practices in different countries; this is called harmonization. In an article in Accounting and Business Research, Emmanuel N. Emenyonu and Sidney J. Gray studied the extent to which accounting practices in France, Germany, and the U.K. are harmonized. (a) Depreciation method is one of the accounting practices studied by Emenyonu and Gray. Three methods were considered—the straight-line method (S), the declining balance method (D), and a combination of D & S(sometimes European firms start with the declining balance method and then switch over to the straight-line method when the figure derived from straight line exceeds that from declining balance). The data in the table (below) summarize the depreciation methods used by a sample of 78 French, German, and U.K. firms. Depreciation Methods France Germany UK Total A. Straight line (S) 15 0 25 40 B. Declining Bal (D) 1 1 1 3 C. (D & S) 10 25…
- In recent years major efforts have been made to standardize accounting practices in different countries; this is called harmonization. In an article in Accounting and Business Research, Emmanuel N. Emenyonu and Sidney J. Gray studied the extent to which accounting practices in France, Germany, and the U.K. are harmonized. (a) Depreciation method is one of the accounting practices studied by Emenyonu and Gray. Three methods were considered—the straight-line method (S), the declining balance method (D), and a combination of D & S(sometimes European firms start with the declining balance method and then switch over to the straight-line method when the figure derived from straight line exceeds that from declining balance). The data in the table (below) summarize the depreciation methods used by a sample of 78 French, German, and U.K. firms. Depreciation Methods France Germany UK Total A. Straight line (S) 15 0 25 40 B. Declining Bal (D) 1 1 1 3 C. (D & S) 10 25…Active Frame, Inc., manufactures clear and tinted sport glasses. The manufacturing of clear glasses takes 45,000 direct labor hours and involves 1,700 parts and 115 inspections. The manufacturing of tinted glasses takes 115,000 direct labor hours and involves 1,400 parts and 450 inspections. The traditional method applies P560,000 of overhead based on direct labor hours. What is the amount of overhead per direct labor hour applied to the clear glass products?17. The Porsche Club of America sponsors driver education events that provide high-performance driving instruction on actual racetracks. Because safety is a primary consideration at such events, many owners elect to install roll bars in their cars. Deegan Industries manufactures two types of roll bars for Porsches. Model DRB is bolted to the car using existing holes in the car’s frame. Model DRW is a heavier roll bar that must be welded to the car’s frame. Model DRB requires 20 pounds of special high-alloy steel, 40 minutes of manufacturing time, and 60 minutes of assembly time. Model DRW requires 25 pounds of the special high-alloy steel, 100 minutes of manufacturing time, and 40 minutes of assembly time. Deegan’s steel supplier indicated that at most 40,000 pounds of the high-alloy steel will be available next quarter. In addition, Deegan estimates that 2000 hours of manufacturing time and 1600 hours of assembly time will be available next quarter. The profit contributions are $200…
- Based on Angel et al. (2003). A fertilizer companyis trying to determine the cheapest fertilizer mix thatprovides desired amounts of nutrients. The mix ismade by combining the following fertilizers: SSA,SPO, GUR, TSP, KCI, FERT, and SPF. The mix cannot contain both GUR and TSP. The percentage ofpotassium (K), sulfur (S), calcium (Ca), sodium (Na)and phosphorus (P) in each fertilizer is listed in the fileP06_88.xlsx. For example, a pound of SSA is 16% Kand 26% Na. The mix must contain at least 600 poundsof K, 550 pounds of S, 750 pounds of Ca, 900 poundsof Na, and 750 pounds of P. The mix cannot containboth GUR and TSP, because if both are present in themix, the affect of other fertilizers is nullified. The costper pound (in cents) of each fertilizer is listed in thesame file. Develop a linear integer model to find theminimum-cost fertilizer mixture that meets the statedchemical requirements.An automobile company produces cars in Los Angeles and Detroit and has a warehouse in Atlanta.The company supplies cars to customers in Houston and Tampa. The costs of shipping a car betweenvarious points are listed in the table below, where a blank means that a shipment is not allowed. LosAngeles can produce up to 1100 cars, and Detroit can produce up to 2900 cars. Houston must receive2400 cars, and Tampa must receive 1500 cars. (Include your formulations to receive credit. Thinkcarefully about the transhipment locations.) (a) Determine how to minimize the cost of meeting demands in Houston and Tampa. (b) Modify the answer to part (a) if shipments between Los Angeles and Detroit are not allowed. (c) Modify the answer to part (a) if shipments between Houston and Tampa are allowed at a cost of$5 per car.A researcher is interested in understanding how the flexibility of vacation policies at a company influence employee satisfaction with their job. Company 1, Vance Refrigeration, has a 2 week vacation policy in which employees can take those 2 weeks at any time during the year. Company 2, Dunder Mifflin Paper Company, has a 2 week vacation policy in which employees can only take vacation days during specific pre-approved times of year. What is the confound?
- I want example of last-come first-served (LCFS)Two different types of polishing solutions are being evaluated for possible use in a tumble-polish operation for manufacturing interocular lenses used in the human eye following cataract surgery. Three hundred lenses were tumble polished using the first polishing solution, and ofthis number, 253 had no polishing-induced defects. Another 300 lenses were tumble-polishedusing the second polishing solution, and 196 lenses were satisfactory upon completion.(a) Is there any reason to believe that the two polishing solutions differ? Use α = 0.01The Grand Canyon and the Colorado River are beautiful, rugged, and sometimes dangerous. Assume there is a physician at the park clinic in Grand Canyon Village. Suppose the physician has recorded (for a 5-year period) the number of visitor injuries at different landing points for commercial boat trips down the Colorado River in both the Upper and Lower Grand Canyon. Upper Canyon: Number of injuries per Landing Point BetweenNorth Canyon and Phantom Ranch 2 3 1 1 3 4 8 11 3 1 3 Lower Canyon: Number of injuries per Landing Point BetweenBright Angel and Lava Falls 10 1 1 0 8 9 2 11 3 0 1 10 2 1 The mean, median, and mode for Upper Canyon are 3.636, 3.0, and 3, respectively. The mean, median, and mode for Lower Canyon are 4.286, 2.0, and 1, respectively.Compare the mean, median, and mode found in Upper Canyon and Lower Canyon, respectively.