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### hw4

Course: MATH 171A, Spring 2012
School: UCSD
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Word Count: 418

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171A: Math Linear Programming Instructor: Philip E. Gill Winter Quarter 2011 Homework Assignment #4 Due Friday February 4, 2011 Starred exercises require the use of Matlab. Exercise 4.1. Suppose that the constant vector c is such that cTp 0 for all p such that Ap = 0. Show that this implies that cTp = 0 for all p such that Ap = 0. Exercise 4.2. Consider the equality-constrained linear program: minimize cTx...

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171A: Math Linear Programming Instructor: Philip E. Gill Winter Quarter 2011 Homework Assignment #4 Due Friday February 4, 2011 Starred exercises require the use of Matlab. Exercise 4.1. Suppose that the constant vector c is such that cTp 0 for all p such that Ap = 0. Show that this implies that cTp = 0 for all p such that Ap = 0. Exercise 4.2. Consider the equality-constrained linear program: minimize cTx subject to Ax = b, where -8 -2 -1 5 0 1 1 4 A= , b= and c = 6 . 3 -1 1 4 2 -5 3 5 (a) Find a feasible point x for this problem. Is it optimal? (b) Find unique vectors cN null(A) and cR range(AT ) such that c = cR + cN . Hence find a feasible direction p such that (x + p) < (x) for all positive . Exercise 4.3. Consider the equality-constrained linear program of minimizing cTx subject to Ax = b. For each of the following instances of A, b and c, determine whether or not the linear program has a solution, If not, explain why not. If so, find a minimizer x and a Lagrange multiplier , and explain whether or not they are unique. 8 -4 2 2 10 1 2 , b = 2 and c = 0 . (a) A= 3 -1 3 1 1 5 2 17 -4 1 3 2 -1 (b) A= , b= and c = -1 . -3 -8 2 6 3 -10 1 9 14 5 (c) A = 3 7 , b = 2 and c = . 3 1 -2 1 (d) The same matrix A and vector b as in part (b), and 1 1 c = . 1 1 2 Mathematics 171A (e) The same matrix A and vector c as in part (c), and 6 b = 3 . 1 Exercise 4.4. Consider the equality-constrained linear program: minimize cTx subject to Ax = b. If this problem has a bounded minimum , show the following: (i) = cTx = cTx for any two feasible points x and x; T T (ii) = b = b for any two sets of Lagrange multipliers and . Exercise 4.5. Consider the equality-constrained linear program: minimize cTx subject to Ax = b. Show that if A has full column rank and b range(A), then this problem always has a unique bounded solution, regardless of the definition of c. Do Lagrange multipliers exist? If they exist, are they unique? Exercise 4.6. Let F denote the feasible region F = {x Rn : Ax = b}, where A be an m n matrix of rank r and b is an m vector. Assume that there is at least one feasible point. Let Ar denote an r n matrix of r linearly independent rows of A and let br denote the corresponding r-vector of right-hand sides. Show that F is identical to the = set Fr {x Rn : Ar x = br }. This problem should be a good test of your linear algebra. Don't worry, it's too tricky ever to be on a test!
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UCSD - MATH - 171A
Math 171A: Linear ProgrammingInstructor: Philip E. GillWinter Quarter 2011Homework Assignment #5 Due Friday February 11, 2011 Starred exercises require the use of Matlab. Exercise 5.1. Consider the set of inequality constraints Ax b, where 1 1 4 0 3 1
UCSD - MATH - 171A
Math 171A: Linear ProgrammingInstructor: Philip E. GillWinter Quarter 2011Homework Assignment #6 Due Friday February 18, 2011 Starred exercises require the use of Matlab. Exercise 6.1. (a) Consider the matrix of active constraints -1 -8 4 -4 2 0 Aa = -
UCSD - MATH - 171A
Math 171A: Linear ProgrammingInstructor: Philip E. GillWinter Quarter 2011Homework Assignment #7 Due Friday February 25, 2011 Starred exercises require the use of Matlab. Exercise 7.1. Consider the linear program of minimizing cTx subject to the genera
UCSD - MATH - 171A
Math 171A: Linear ProgrammingInstructor: Philip E. GillWinter Quarter 2011Homework Assignment #8 Due Friday March 4, 2011 The second midterm exam will be held in class on Wednesday, March 2. Starred exercises require the use of Matlab. Exercise 8.1. Co
UCSD - MATH - 171A
Math 171A: Linear ProgrammingInstructor: Philip E. GillWinter Quarter 2011Homework Assignment #9 Due Friday March 11, 2011 The final will be held Friday, March 18, 11:30am-2:30pm. Starred exercises require the use of Matlab. Exercise 9.1. Let a denote
Cal Poly - MCB - 32
1. The Cori cycle involves formation of glucose made by gluconeogenesis in the liver from lactic acid produced by fermentation in skeletal muscles. True False 2. Skeletal muscle contains glucose 6-phosphatase to produce free glucose from glucose 6phosphat
Cal Poly - MCB - 32
Chapter 15 - Defense Mechanisms I. Nonspecific defense: barriers to penetration of body/ A. Antigens large, complex, and foreign molecules internal defenses. B. Antigenic determinant sites stimulate production of diff. A. Phagocytic cells engulf invading
Cal Poly - MCB - 32
Glomerular Filtration I. Filtrate from plasma in glomerulusbasement mem of glom cap/ thru slits in processes of podocytes (inner layer of Bowman's capsule) A. Glomerular ultrafiltrate, formed under force of bp, low [protein] net filtration pressure = 10 m
Cal Poly - MCB - 32
AdrenergicEpinephrine, norepinephrine - Sympathetic &quot;fight or flight&quot; - Effects = stimulation of heart, vasoconstriction of skin, bronchodilation, glycogenolysis - alpha and beta (both have 2 subtypes) Nerve endings that release acetylcholine as a neurot
Cal Poly - MCB - 32
Number and Name I Olfactory II Optic III Oculomotor IV Trochlear V Trigeminal Mandibular Division VI Abducens VII Facial VIII Vestibulocochlear IX Glossopharyngeal X Vagus XI Accessory XII Hypoglossal Endocrine Gland Adipose Tissue Adrenal Cortex Adrenal
Cal Poly - MCB - 32
Number and Name I Olfactory II Optic III Oculomotor IV Trochlear V Trigeminal Mandibular Division VI Abducens VII Facial VIII Vestibulocochlear IX Glossopharyngeal X Vagus XI Accessory XII Hypoglossal Endocrine Gland Adipose Tissue Adrenal Cortex Adrenal
Cal Poly - MCB - 32
Guided Reading The Study of Body Function I 1. Blood plasma and interstitial fluid are separated from each other and there is little communication and exchange between these fluids. True False 2. The secretion of many hormones is regulated through negativ
Cal Poly - MCB - 32
Guided Reading - Enzymes and Energy I 1. Regulation of a metabolic pathway by the final product of the pathway is termed A. allosteric inhibition. B. end-product inhibition. C. negative feedback. D. Both end-product inhibition and negative feedback are co
Cal Poly - MCB - 32
Guided Reading - Cells and the Extracellular Environment I 1. Which of the following is a function of the steep Na+/K+ gradient across the cell membrane? A. provides energy for coupled transport B. creates electrochemical impulses C. maintains osmotic pre
Cal Poly - MCB - 32
Guided Reading - Cell Respiration and Metabolism I1. _ is the opposite of glycogenesis. A. Glycolysis B. Glyconeogenesis C. Glycogenolysis D. Gluconeogenesis 2. The process of fat formation from acetyl CoA is called A. lipogenesis. B. lipolysis. C. beta-
Cal Poly - MCB - 32
Guided Reading - Cell Respiration and Metabolism II1. Which of the following is a superoxide radical? A. an oxygen molecule with an extra, unpaired electron B. an oxygen molecule with two paired electrons C. hydrogen peroxide D. All of these choices are
Cal Poly - MCB - 32
Guided Reading - Cell Respiration and Metabolism II1. Which of the following is a superoxide radical? A. an oxygen molecule with an extra, unpaired electron B. an oxygen molecule with two paired electrons C. hydrogen peroxide D. All of these choices are
Cal Poly - MCB - 32
Guided Reading - Cell Respiration and Metabolism III1. Glycolysis converts glucose into two _ molecules. A. glycogen B. lactic acid C. acetyl CoA D. pyruvic acid2. Beta-oxidation of an 18 carbon fatty acid will yield _ acetyl CoA molecules. A. 9 B. 6 C.
Cal Poly - MCB - 32
Guided Reading - Cell Respiration and Metabolism III1. Glycolysis converts glucose into two _ molecules. A. glycogen B. lactic acid C. acetyl CoA D. pyruvic acid2. Beta-oxidation of an 18 carbon fatty acid will yield _ acetyl CoA molecules. A. 9 B. 6 C.
Cal Poly - MCB - 32
Guided Reading - Cell Structure and Genetic Control I1. Cells actively involved in secreting proteins would contain large numbers or quantities of A. lysosomes. B. peroxisomes. C. rough endoplasmic reticulum. D. smooth endoplasmic reticulum.2. Release o
Cal Poly - MCB - 32
Guided Reading - Cell Structure and Genetic Control I1. Cells actively involved in secreting proteins would contain large numbers or quantities of A. lysosomes. B. peroxisomes. C. rough endoplasmic reticulum. D. smooth endoplasmic reticulum.2. Release o
Cal Poly - MCB - 32
Guided Reading - Cell Structure and Genetic Control II1. Which of the following is NOT a molecular motor used to move substances along the cytoskeleton? A. melanin B. kinesin C. myosin D. dynein2. Which of the following locations have ciliated cells? A.
Cal Poly - MCB - 32
Guided Reading - Cell Structure and Genetic Control II1. Which of the following is NOT a molecular motor used to move substances along the cytoskeleton? A. melanin B. kinesin C. myosin D. dynein2. Which of the following locations have ciliated cells? A.
Cal Poly - MCB - 32
Guided Reading - Cell Structure and Genetic Control III1. The movement of chromosomes during mitosis is due to A. spindle fibers. B. telomeres. C. chromatids. D. actin and myosin.2. Small RNA and protein regions are joined together to make functional mR
Cal Poly - MCB - 32
Guided Reading - Cell Structure and Genetic Control IV1. The main function of the peroxisome is to release energy from food molecules and transform the energy into usable ATP. True False 2. Microtubules and microfilaments are the primary components of th
Cal Poly - MCB - 32
Guided Reading - Cells and the Extracellular Environment I1. Which of the following is a function of the steep Na+/K+ gradient across the cell membrane? A. provides energy for coupled transport B. creates electrochemical impulses C. maintains osmotic pre
Cal Poly - MCB - 32
Guided Reading - Cells and the Extracellular Environment II 1. Edema will result if a person has an abnormally low concentration of plasma proteins. True False 2. Osmoreceptors are involved in the regulation of blood volume. True False 3. Ion channels tha
Cal Poly - MCB - 32
Guided Reading Cells and the Extracellular Environment III1. The resting membrane potential is closest to the equilibrium potential for A. sodium ions. B. chloride ions. C. calcium ions. D. potassium ions.2. The transport maximum is related to the prope
Cal Poly - MCB - 32
Guided Reading - Cells and the Extracellular Environment IV 1. Which of the following is NOT a primary active transport pump? A. GLUT4 B. calcium pump C. sodium/potassium pump D. proton pump 2. What cofactor do matrix metalloproteinases need to be functio
Cal Poly - MCB - 32
Guided Reading - Chemical Composition of the Body I1. Molecules with polar covalent bonds are hydrophobic. True False2. How many single bonds can a carbon atom form if it is double-bonded to an oxygen atom? A. 1 B. 2 C. 3 D. 43. The ionized form of the
Cal Poly - MCB - 32
Guided Reading - Chemical Composition of the Body II1. Steroids are derived from cholesterol. True False 2. A blood pH of 7.6 is A. indicative of acidosis. B. indicative of alkalosis. C. in the normal physiological range. D. indicates effective buffering
Cal Poly - MCB - 32
Guided Reading - Chemical Composition of the Body III1. Lipids containing glycerol would include _ and _. A. triglycerides, steroids B. prostaglandins, phospholipids C. triglycerides, phospholipids D. steroids, prostaglandins2. The base that is NOT foun
Cal Poly - MCB - 32
Guided Reading - Enzymes and Energy I1. Regulation of a metabolic pathway by the final product of the pathway is termed A. allosteric inhibition. B. end-product inhibition. C. negative feedback. D. Both end-product inhibition and negative feedback are co
Cal Poly - MCB - 32
Guided Reading - Enzymes and Energy II1. Isomers are different forms of an enzyme. True False 2. During oxidation, a molecule or atom A. gains protons. B. loses protons. C. gains electrons. D. loses electrons. 3. Oxidized nicotinamide adenine dinucleotid
Cal Poly - MCB - 32
Guided Reading - Enzymes and Energy III1. Catalysts increase reaction rates by lowering the activation energy of a reaction. True False2. An enzyme elevated in the plasma of men with prostate cancer is A. alkaline phosphatase. B. catalase. C. creatine k
Cal Poly - MCB - 32
Guided Reading The Study of Body Function I1. Blood plasma and interstitial fluid are separated from each other and there is little communication andexchange between these fluids.True False2. The secretion of many hormones is regulated through negativ
Cal Poly - MCB - 32
Guided Reading - The Study of Body Function II1. Which of the following is NOT a major organ of the circulatory system?A. spleenB. heartC. lymphatic vesselsD. blood vessels2. Endocrine gland secretion is often controlled by the nervous system.True
Cal Poly - MCB - 32
Guided Reading - The Study of Body Function III1. Enamel, which is harder than bone or dentin, cannot be regenerated. True False2. Aristotle is considered the father of physiology because he attempted to apply physical laws to the study of human functio
Cal Poly - MCB - 32
Guided Reading - The Autonomic Nervous System I - Key1. Damage to the autonomic motor nerves would probably result in A. no change in muscle tone. B. muscle atrophy. C. flaccid paralysis. D. increased skeletal muscle contraction.Blooms Level: 2. Underst
Cal Poly - MCB - 32
Guided Reading - The Autonomic Nervous System I 1. Damage to the autonomic motor nerves would probably result in A. no change in muscle tone. B. muscle atrophy. C. flaccid paralysis. D. increased skeletal muscle contraction. 2. Damage to the thoracic and
Cal Poly - MCB - 32
Guided Reading - Blood, Heart, and Circulation I 1. Endogenously applied _ or tissue plasminogen activator (TPA) can induce blood clot dissolution. A. albumin B. streptokinase C. thromboxane A2 D. penicillin 2. What type of cell found in the blood produce
Cal Poly - MCB - 32
Guided Reading - Cardiac Output, Blood Flow, and Blood Pressure I 1. The type of shock resulting from lipopolysaccharides is termed A. hypovolemic shock. B. cardiogenic shock. C. septic shock. D. neurogenic shock. 2. Hypotension could be induced by A. exc
Cal Poly - MCB - 32
Blood, Heart, and Circulation Key101. Which anticoagulant and its action is NOT correctly matched? A. aspirin - inhibits prostaglandin production and platelet aggregation B. heparin - inhibits action of thrombin C. coumadin - inhibits tissue thromboplast
Cal Poly - MCB - 32
Guided Reading - The Central Nervous System I 1. _% of total blood flow to the body per minute goes to the brain. A. 15 B. 20 C. 25 D. 30 2. The neural tube and neural crest cells are of endodermal origin. True False 3. Ataxia is often associated with A.
Cal Poly - MCB - 32
Guided Reading - Endocrine Glands I 1. What is the function of prolactin in females? A. stimulates milk production in the mammary glands B. regulates the gonadotropins C. regulates water and electrolyte balance in the kidneys D. All of the choices and cor
Cal Poly - MCB - 32
Guided Reading - Blood, Heart, and Circulation I1. Endogenously applied _ or tissue plasminogen activator (TPA) can induce blood clot dissolution. A. albumin B. streptokinase C. thromboxane A2 D. penicillin2. What type of cell found in the blood produce
Cal Poly - MCB - 32
Guided Reading - Blood, Heart, and Circulation II1. Which vessels are most important for controlling resistance to blood flow? A. elastic arteries B. venules C. capillaries D. arterioles2. The lymphatic system can help cancer _ since cancer cells may en
Cal Poly - MCB - 32
Guided Reading - Blood, Heart, and Circulation III1. Myocardial cells exhibit a plateau phase instead of quickly repolarizing. This is due to A. inward diffusion of calcium through slow Ca2+ channels. B. inward diffusion of sodium through fast Na+ channe
Cal Poly - MCB - 32
Guided Reading - Blood, Heart, and Circulation IV1. What is the role of serotonin in blood clotting? A. causes platelets to become sticky B. enhances the platelet release reaction C. causes vasoconstriction of blood vessels to slow loss of blood D. conve
Cal Poly - MCB - 32
Guided Reading - Blood, Heart, and Circulation V1. Which anticoagulant and its action is NOT correctly matched? A. aspirin - inhibits prostaglandin production and platelet aggregation B. heparin - inhibits action of thrombin C. coumadin - inhibits tissue
Cal Poly - MCB - 32
Guided Reading - Cardiac Output, Blood Flow, and Blood Pressure III1. The sounds heard during the first phase of blood-pressure measurement are A. murmurs. B. snapping sounds. C. thumping sounds. D. muffled thumping sounds.2. Blood volume would be incre
Cal Poly - MCB - 32
Guided Reading - Cardiac Output, Blood Flow, and Blood Pressure I1. The type of shock resulting from lipopolysaccharides is termed A. hypovolemic shock. B. cardiogenic shock. C. septic shock. D. neurogenic shock.2. Hypotension could be induced by A. exc
Cal Poly - MCB - 32
Guided Reading - Cardiac Output, Blood Flow, and Blood Pressure II1. Sympathetic stimulation promotes an overall increase in blood flow resistance. True False2. At rest, most blood is within the venous system. True False3. The effect of acetylcholine b
Cal Poly - MCB - 32
Guided Reading - Cardiac Output, Blood Flow, and Blood Pressure IV1. The ability to distend with pressure increases is called A. chronotropism. B. oncotism. C. inotropism. D. compliance. 2. Angiotensin-converting enzyme (ACE) inhibitors like captopril bl
Cal Poly - MCB - 32
Guided Reading - Cardiac Output, Blood Flow, and Blood Pressure V1. Vasodilation is induced by all of the following EXCEPT A. increased tissue carbon dioxide. B. decreased tissue metabolism. C. decreased tissue oxygen. D. increased extracellular K+.2. A
Cal Poly - MCB - 32
Guided Reading - Endocrine Glands I1. What is the function of prolactin in females? A. stimulates milk production in the mammary glands B. regulates the gonadotropins C. regulates water and electrolyte balance in the kidneys D. All of the choices and cor
Cal Poly - MCB - 32
Guided Reading - Endocrine Glands II1. Cortisol secretion would cease if the _ no longer secreted ACTH. A. posterior pituitary gland B. hypothalamus C. anterior pituitary gland D. adrenal cortex 2. What controls release of corticoids from the adrenal cor
Cal Poly - MCB - 32
Guided Reading - Endocrine Glands III1. What hormone(s) is/are released when blood glucose levels decrease? A. insulin B. glucagon C. glucocorticoids D. both glucagon and glucocorticoids2. A tumor stimulating oversecretion of hormones by the thyroid gla
Cal Poly - MCB - 32
Guided Reading - Endocrine Glands IV1. Which of the following is true of parathyroid hormone function? A. It causes the kidneys to reabsorb calcium. B. It causes the dissolution of calcium phosphate from bones. C. It increases blood calcium levels. D. Al
Cal Poly - MCB - 32
Guided Reading - Endocrine Glands V1. _ inhibits COX3 in the brain which results in pain and fever reduction. A. Acetaminophen (Tylenol) B. Aspirin C. Ibuprofen (Motrin) D. All of the choices are correct.2. The same prostaglandin may produce different e
Cal Poly - MCB - 32
Guided Reading Muscle: Mechanisms of Contraction and Neural Control I1. The pyramidal tracts include the _ and _ tracts. A. rubrospinal, lateral corticospinal B. reticulospinal, ventral corticospinal C. ventral corticospinal, lateral corticospinal D. rub