exam1_sol_f01

合集下载

Exam4_1说明

第4章视图与对话框4.1.3编程实例【例4-1】本例将设计一个简单的文本编辑器（不使用CEditView类），用以说明文档/视图的原理及应用。

在这个编辑器中，用户只能逐行输入字符，按回车键结束一行并换行，不支持字符的删除和插入，也没有光标指示当前编辑位置。

但是用户可以选择编辑器显示文本所使用的字体。

实验步骤：1．生成项目使用AppWizard生成编辑器程序的框架，项目名为Exam4_1。

在MFC AppWizard-step 1选择Single Document；在MFC AppWizard 4 of 6的对话框中，单击Advanced按钮，弹出Advanced Option对话框，如图4-6所示，该对话框设置文档/视图结构和主框架窗口的一些属性。

图4-6 Advanced Option 对话框该对话框有两个标签页，一页是Document Template Strings，用于设置文档/视图结构的一些属性，该项的值将与应用程序类中定义文档模板类对象的第一个参数IDR_MAINFRAME对应，它包括以下几个文本框：(1)File extersion指定应用程序创建的文档所用的文件名的后缀。

输入后缀名txt。

(2)File type ID用于在Windows的注册数据库中标识应用程序的文档类型。

(3)Main frame caption主框架窗口标题，默认情况下与项目名相一致。

(4)Doc type name该文档类型名，指定与一个从CDocument派生的文档类相关的文档类型名。

(5)Filter name用作“打开文件”、“保存文件”对话框中的过滤器。

Visual Studio会自动根据输入的后缀名生成一个过滤器：Exam4_1 文件(*.txt)。

这样当在Open File对话框中选择Exam4_1 文件(*.txt)时，只有以txt 为后缀名的文件名显示在文件名列表中。

(6)File new name(short name)用于指定在new对话框中使用的文档名。

STAT7055_2013-S1_MS-exam_sol

STAT7055
Mid-Semester Examination First Semester 2013
Page 3 of 9
(e) [5 marks] Find the probability distribution of X . Solution: The possible values X can take are 0, 1, and 2. We can ﬁnd the corresponding probabilities as follows: P (X = 2) = P (A ∩ B ) = 0.06 P (X = 1) = P (A ∩ B C ) + P (AC ∩ B ) = 0.14 + (P (B ) − P (A ∩ B )) = 0.14 + (0.6 − 0.06) = 0.68 P (X = 0) = 1 − 0.06 − 0.68 = 0.26 (f) [2 marks] Find the expected value of X . Solution: E (X ) =
= 1.645 ∴ n = 43.2964 ≈ 44
Question 3 [13 marks]
Suppose X is a uniformly distributed random variable between a and b and Y is a uniformly distributed random variable between b and b + 1. (a) [2 marks] If the expected value of X is E (X ) = 34.5 and the expected value of Y is E (Y ) = 42, ﬁnd the values of a and b. Solution: +1 b and E (Y ) = 2b2 , setting each of these to their given expected Since E (X ) = a+ 2 values and solving for a and b, we get a = 27.5 and b = 41.5. Note that for parts (b) through (e), if you did not answer part (a), use the following values: a = 28 and b = 42. Otherwise, please use the values you calculated in part (a). (b) [2 marks] Calculate the probability that X lies between 33.33 and 40.27. Solution: P (33.33 < X < 40.27) = 1 × (40.27 − 33.33) = 0.4957 14

SampleExam01(Ch1, 2)

Part I: Multiple Choice Questions: (1 pt each)5 quizzes for Chapter 11 Java ___________ can run from a Web browser.A. applicationsB. Micro Edition programsC. servletsD. applets2 Which of the following statements is true?A. A Java applet can be executed from a Web browser.B. A Java application can be executed from a Web browser.3 The hex value 7A is __________ in binary.A. 1111110B. 10111010C. 1111011D. 1111010E. 111101014 Java is an object-oriented programming language.A. trueB. false5 The binary representation of decimal 49 is ______.A. 110011B. 110001C. 110000D. 110101E. 11100120 quizzes for Chapter 26 Math.pow(2, 3) returns __________.A. 8;B. 8.0;C. 9;D. 9.0;7 To improve readability and maintainability, you should declare_________ instead of using literal values such as 3.14159.A. constantsB. variablesC. classesD. methods8 Which of the following expression results in a value 1?A. 37 % 6B. 25 % 5C. 15 % 4D. 2 % 19 The Unicode of 'a' is 97. What is the Unicode for 'c'?A. 96B. 98C. 97D. 9910 A Java character is stored in __________.A. four bytesB. two bytesC. three bytesD. one byte11 If you attempt to add an int, a byte, a long, and a double, the result will be a __________ value.A. longB. byteC. doubleD. int12 What is y displayed?public class Test {public static void main(String[] args) {int x = 1;int y = x + x++;System.out.println("y is " + y);}}A. y is 2.B. y is 1.C. y is 4.D. y is 3.13 The expression (int)(76.0252175 * 100) / 100 evaluates to_________.A. 76.03B. 76.0252175C. 76.02D. 7614 According to Java naming convention, which of the following names can be variables?A. classB. totalLengthC. TOTAL_LENGTHD. FindAreaE. findArea15 Which of the following are correct names for variables according to Java naming conventions?A. RADIUSB. findAreaC. radiusD. RadiusE. FindArea16 To assign a value 1 to variable x, you writeA. x := 1;B. 1 := x;C. 1 = x;D. x == 1;E. x = 1;17 The __________ method parses a string s to a double value.A. double.parse(s);B. Double.parsedouble(s);C. double.parseDouble(s);D. Double.parseDouble(s);18 To add number to sum, you write (Note: Java is case-sensitive)A. sum = Number + sum;B. number += sum;C. number = sum + number;D. sum += number;E. sum = sum + number;19 Suppose a Scanner object is created as follows:Scanner scanner = new Scanner(System.in);What method do you use to read an int value?A. scanner.nextInteger();B. scanner.integer();C. scanner.int();D. scanner.nextInt();20 An int variable can hold __________.A. 120.0B. 'x'C. "120"D. 120E. "x"21 Which of the following operators has the highest precedence?A. +B. castingC. *D. /22 Which of the following is a constant, according to Java naming conventions?A. ReadIntB. readC. MAX_VALUED. Test23 A variable may be assigned a value only once in the program.A. falseB. true24 You can define a constant twice in a block.A. trueB. false25 A Java statement ends with a __________.A. period (.)B. closing braceC. semicolon (;)D. comma (,)Part II: Find and correct errors in the following code: (5 pts)public class Test {public void Main(String[] args) {int j = i + 1;int k = 5.5;System.out.println("j is " + j + "andk is " + k);}}Part III: Show the output of the following code:(5 pts)public class Test {public static void main(String[] args) {int x1, x2, i, j, k, y, z;float f;x1 = 1;x2 = 1;y = 5 + x1--;z = 5 + ++x2;i = 6 % 4;j = 1;j += j + 3;k = 25 / 2;f = (float)((2 / 5) * k);System.out.println("x1 is " + x1);System.out.println("x2 is " + x2);System.out.println("i is " + i);System.out.println("j is " + j);System.out.println("k is " + k);System.out.println("y is " + y);System.out.println("z is " + z);System.out.println("f is " + f);}}Key for Exam 1Part I: Multiple Choice Questions: (1 pt each)Keys:1. D2. A3. D4. A5. B6. B7. A8. A9. D10. B11. C12. A13. D14. BE15. BC16. E17. D18. DE19. D20. BD21. B22. C23. A24. B25. CPart II: Find all syntax errors in the following code: (Please turn Word Reviewing to(5 pts)public class Test{public void main(String[] args){int i = 0;int j = i + 1;int k = (int)5.5;System.out.println("j is " + j + "and k is " + k);}}Part III: Show the output of the following code:(5 pts)public class Test {public static void main(String[] args) {int x1, x2, i, j, k, y, z;float f;x1 = 1;x2 = 1;y = 5 + x1--;z = 5 + ++x2;i = 6 % 4;j = 1;j += j + 3;k = 25 / 2;f = (float)((2 / 5) * k);System.out.println("x1 is " + x1);System.out.println("x2 is " + x2);System.out.println("i is " + i);System.out.println("j is " + j);System.out.println("k is " + k);System.out.println("y is " + y);System.out.println("z is " + z);System.out.println("f is " + f);}}x1 is 0x2 is 2i is 2j is 5k is 12y is 6z is 7f is 0.0Part IV: Write a complete program named Exam1.java. The program reads three double numbers from the keyboard and displays the average of these three numbers.(5 pts)import java.util.Scanner;public class Test {/**Main method*/public static void main(String[] args) {Scanner input = new Scanner(System.in);// Prompt the user to enter an integerSystem.out.print("Enter number1:");int number1 = input.nextInt();System.out.print("Enter number2:");int number2 = input.nextInt();System.out.print("Enter number3:");int number3 = input.nextInt();// Display resultsSystem.out.println("The average is " + (number1 + number2 + number3) / 3); }}。

SOL语言练习试卷2(题后含答案及解析)

SOL语言练习试卷2(题后含答案及解析)全部题型 3. 主观题主观题工厂的信息管理数据库中有两个关系模式：职工(职工号，姓名，年龄，月工资，部门号，电话，办公室) 部门(部门号，部门名，负责人代码，任职时间)1．查询每个部门中月工资最高的“职工号”的SQL查询语句如下：SELECT 职工号FROM 职工 E WHERE 月工资=(SELECT MAX(月工资) FROM 职工AS M WHERE M．部门号=E．部门号); ①请用30字以内的文字简要说明该查询语句对查询效率的影响。

②对该查询语句进行修改，使它既可以完成相同功能，又可以提高查询效率。

正确答案：此问考查的是查询效率的问题。

在涉及相关查询的某些情形中，构造临时。

关系可以提高查询效率。

①对于外层的职工关系E中的每一个元组，都要对内层的整个职工关系M进行检索，因此查询效率不高。

②解答方法一(先把每个部门最高工资的数据存入临时表，再对临时表进行查询)：SELECT MAX (月工资) As最高工资，部门号Into Temp FROM 职工GROUP BY 部门号; SELECT 职工号FROM 职工，Temp WHERE 月工资=最高工资AND职工．部门号=Temp．部门号; 解答方法二(直接在FROM 子句中使用临时表结构)：SELECT 职工号FROM职工，(SELECT MAX(月工资) As最高工资，部门号FROM 职工GROUP BY 部门号) As depMax WHERE 月工资=最高工资AND职工．部门号=depMax．部门号; 涉及知识点：SOL语言2．假定分别在“职工”关系中的“年龄”和“月工资”字段上创建了索引，如下的Select查询语句可能不会促使查询优化器使用索引，从而降低了查询效率，请写出既可以完成相同功能又可以提高查询效率的SQL语句。

SELECT 姓名，年龄，月工资FROM职工WHERE 年龄＞45 OR月工资＜1000;正确答案：此问主要考察在查询中注意WHERE子句中使用索引的问题。

CLAD Sample Exam-1

LabVIEW助理开发工程师考试为了快速找到问题，可将答案记录在本页答题纸上。

撕下该页用于记录答案。

实际的CLAD考试中并无该页，仅供模拟题使用。

答案页在模拟题的最后。

1._____2._____3._____4._____5._____6._____7._____8._____9._____10._____11._____12._____13._____14._____15._____16._____17._____18._____19._____20._____21._____22._____23._____24._____25._____26._____27._____28._____29._____30._____31._____32._____33._____34._____35._____36._____37._____38._____39._____40._____1.如要考虑状态图应用程序的扩展性，基本结构的最佳选择是？a.顺序结构b.条件结构c.公式节点d.面向对象的结构2.单击_________按钮可跳过程序框图上的节点，而不单步执行该节点。

a.单步步入b.单步步过c.单步步出d.单步调试3.下列关于属性节点的描述，正确的选项有哪些？（选择所有正确的选项）a.属性节点使用户可通过程序方式操控前面板对象。

b.属性节点可用于更新前面板的值。

c.一个前面板对象可有多个属性节点。

d.子VI中包含的属性节点使前面板始终加载至内存。

4.必须从子VI中控制顶层VI的一个前面板控件。

必须传递什么到子VI？a.控件的属性b.控件的方法c.控件的引用d.控件的数据类型5.VI执行后，值输出显示控件显示的值是多少？a.0b. 4c. 5d. 66.在条件结构的假(FALSE)分支的代码中设置断点。

如执行条件结构的真(TRUE)分支，VI执行会暂停吗？a.会b.不会7.哪个属性节点改变子VI中数字数值控件的文本颜色属性？a.b.c.d.8.哪种图表更新模式适合从左到右连续显示数据？a.带状图b.示波器图c.扫描图d.步骤图9.下列哪项不符合数据流编程模型？a.移位寄存器b.隧道c.子VId.局部变量10.如有需要，可将顺序结构替换为下列哪项？a.事件结构b.For循环c.状态机d.While循环11.关于下列代码的陈述，正确的是？a.循环执行1次，循环显示控件显示值1b.循环执行1次，循环显示控件显示值0c.循环无限执行，程序必须中止d.循环不执行，循环显示控件显示值012.与下列代码等价的公式是？a.b.c.d.13.某VI启用了自动错误处理，并调用了一个未启用自动错误处理的子VI。

Exam(可查字典)

NCCU Programming Languages MidTerm Exam(可查字典) 樣題與考古題，不含OO部分學號: 姓名:I. True or False questions. (O or X)(a)( ) 高階語言比組合語言有較好的可攜性.(b)( ) C語言不可以採用interpreter的實作方式.(c)( ) Both Prolog and FORTRAN are called imperative languages.(d)( ) C語言的程式由一組functions組成，所以C是functional language。

(e)( ) Fortran does not support recursion because it does not have dynamic memory allocation functionlike C’s malloc.(f)( ) C語言的”static”宣告的目的在於控制變數的記憶體位置大小。

(g)( ) 沒有指標的程式語言就不會有aliasing problem (aliases).(h)( ) Explicit dynamic memory allocation through operations such as malloc are typically done on the heap.(i)( ) If we remove the malloc and free functions from C, then C programs won't have garbage.(j)( ) A partial function from A to B is the same as a total function from a subset of A to B.(k)( ) Scheme語言採取的是dynamic type binding。

exam1

1.The science of statistics includes which of the following: Organizing, Presenting, Interpreting,Collecting, analyzing data is making more effective decisions.2.In descriptive statistics our main objective is to Describe the data we collected.( organize, summarize,present)3.Which of the following statements is true regarding a population? It is a collection individuals, objects,or measurements4.Which of the following statements is true regarding a sample? It is a part of population.5. A qualitative variable Is not numeric.6. A discrete variable is Can assume only certain clearly separated values.7. A nominal scale variable is Usually the result of counting something.8.The ratio scale of measurement Has a meaningful zero point.9.The ordinal scale of measurement Is based on ranks10.Which of the following is an example of a continuous variable? Amount of rainfall in Plano, Texas, lastyear.11.In a frequency distribution the categories must Be mutually exclusive.12.To determine the class interval Find the difference between consecutive lower class limits13.The class frequency is The number of observations in each class14.A research organization is making a study of the selling price of home computers. There are 45computers in the study. How many classes would you recommend? 615.To find the class midpoint Divide the class interval in half and add the result to the lower limit16.Which of the following is not a guideline for a frequency distribution? Have more than 5 observations ineach class17.To convert a frequency distribution to a relative frequency distribution Divide the class frequency by thetotal number of observations18.In a line chart the horizontal axis: Usually involves time, such as months or years19.The difference between a histogram and a frequency polygon is The histogram employs bars whereasthe midpoints are connected for a frequency polygon20.In a cumulative frequency polygon We add the class frequencies starting with the first class21.A difference between calculating the sample mean and the population mean is Only in the symbols, weuse "X bar" instead of µ and n instead of N. Where "X bar" means X with a bar on the top.22.Which of the following measures of location is affected most by extreme values? Mean23.In a set of observations, which measure of central tendency reports the value that occurs most often?Mode24.The weighted mean is a special case of the Mean25.The relationship between the geometric mean and the arithmetic mean is The geometric mean will beequal to or less than the mean26.Suppose you compare the mean of raw data and the mean of the same raw data grouped into a frequencydistribution. These two means will be Approximately equal27.In a set of 10 observations the mean is 20 and the median is 15. There are 2 values that are 6, and allother values are different. What is the mode? 628.Which of the following is a measure of dispersion? Range Variance Standard deviation29.The standard deviation is Based on squared deviations from the mean In the same units as the meanUses all the observations in its calculation30.The variance is Found by squaring the standard deviation31.In a positively skewed distribution The standard deviation cannot be negative32.The mean deviation is Based on absolute values33.The difference between a histogram and a bar chart is: The bars must be next to each other on ahistogram and separated in a bar chart34.In a frequency table: The data is qualitative The categories must be mutually exclusive The categoriesmust be exhaustive35.Do you know "stem-and-leaf display"? Arrange the leaf values from smallest to largest36.What is "Dot Plots"? A histogram groups data into classes. To develop a dot plot we simply display adot for each observation along a horizontal number line indicating the possible values of the data.37.What is the “percentiles”? Percentiles divide a set of observations into 100 equal parts.38.The L.L. Bean men's cotton chambray shirt comes in six colors (blue, stone, rust, green, plum, andindigo), five sizes (S, M, L, XL, and XXL), and two styles (short sleeve and long sleeve). How many different shirts are there? 6039.Anthony's Pizza offers free delivery of their pizza. The following summary information concerns thetime of deliveries: mean time is 30 minutes, media time is 28 minutes, the first quartile is 22 minutes, and the third quartile is 35 minutes. The standard deviation of the delivery times is Cannot bedetermined from the information given40.The quartile deviation is Based on the middle 50 percent of the observations41.In a symmetric distribution The mean, median, and mode are equal42.A coefficient of skewness of -2.73 was computed for a set of data. We conclude that The median islarger than the mean43.A scatter diagram: Is a graphic tool designed to portray the relationship between variables Uses intervalor ratio scale data44.Anthony's Pizza offers free delivery of their pizza. The following summary information concerns thetime of deliveries: mean time is 20 minutes, media time is 18 minutes, the first quartile is 12 minutes, and the third quartile is 25 minutes. What percent of the deliveries take more than 12 minutes? 7545.Which of the following is a correct statement about a probability? It may range from 0 to 146.An experiment is a The act of taking a measurement or the observation of some activity47.Which of the following is a type of probability? Subjective Relative frequency Classical48.Events are independent if The probability of one event happening does not affect the probability ofanother event happening.49.The Special Rule of Addition is used to combine Mutually exclusive events50.We use the General Rule of Multiplication to combine Events that are not independent51.When we find the probability of an event happening by subtracting the probability of the event nothappening from 1, we are using The complement rule52.When we determine the number of combinations The order of the outcomes is not important.53.A stock analyst, based on her experience, estimates the probability a particular stock will increase by$10.00 this year is .30. This is an example of which type of probability? SubjectiveStatistics: The science of collecting, organizing, presenting, analyzing, and interpreting data to assist in making more effective decisions.Descriptive statistics: Methods of organizing, summarizing, and presenting data in an informative way.Inferential statistics: the methods used to estimate a property of a population on the basis of a sample. Population: the entire set of individuals or objects of interest or the measurements obtained from all individuals or objects of interest.Sample: a portion, or part, of the population of interest.Types of variables: qualitative: hair color or brand of PC. Quantitative : discrete –children in a family. Continuous: amount of income tax paid.Levels of measurement: 1. Nominal-data may only be classified- Make of car. 2. Ordinal-Data are ranked-your rank in class. 3. Interval -meaningful difference between values- temperature. 4. Ratio-Meaningful 0 point and ratio between values-number of patients seen.Frequency table: a grouping of qualitative data into mutually exclusive classes showing the number of observations in each class.Frequency distribution: a grouping of data into mutually exclusive classes showing the number of observations in each class.Decide on the number of classes: 2k>= nDetermine the class interval or width= I >= (H-L)/k。

MIT算法导论quiz1_sol

2
You need not justify your answers. (a) Binary search
Solution:
T (n) = T (n/2) + �(1) = �(rt
Solution: T (n) = T (n − 1) + �(n) = �(n2 )
1 1 1 0
�
.
Handout 14: Quiz 1 Solutions
6
T F Suppose that an array contains n numbers, each of which is −1, 0, or 1. Then, the array can be sorted in O (n) time in the worst case. Solution: True. We may use counting sort. We ﬁrst add 1 to each of the elements in the input array such that the precondition of counting sort is satisﬁed. After running counting sort, we subtract 1 from each of the elements in the sorted output array. A solution based on partitioning is as follows. Let A[1 . . n] be the input array. We deﬁne the invariant •A[1 . . i] contains only −1, •A[i + 1 . . j ] contains only 0, and •A[h . . n] contains only +1.

1、下载文档前请自行甄别文档内容的完整性，平台不提供额外的编辑、内容补充、找答案等附加服务。
2、"仅部分预览"的文档,不可在线预览部分如存在完整性等问题,可反馈申请退款(可完整预览的文档不适用该条件!)。
3、如文档侵犯您的权益，请联系客服反馈,我们会尽快为您处理(人工客服工作时间：9:00-18:30)。

Name Davidson College Mark C. Foley Department of Economics Fall 2001

Intermediate Microeconomic Theory Review #1

Selected Suggested Solutions 2 Section I: Multiple Choice Indicate the best answer in the space provided to the right of each question.

1. If both supply and demand decrease at the same time, which of the following B must also decrease? (a) the equilibrium price (b) the equilibrium quantity (c) the use of substitutes (d) the use of complements (e) none of the above

2. The assumption of nonsatiation says that C (a) to consume more of one good, we must give up consumption of a second good. (b) more consumption will decrease total utility. (c) more of anything is always better. (d) more consumption will not lead to a change in total utility. (e) consumers reach a point where they cannot consume more of anything.

3. Jane consumes only xylophones and yams. If we graph Jane’s indifference D curves with xylophones on the horizontal axis and yams on the vertical axis, then whenever she has more yams than xylophones, the slope of her indifference curves are –2. Whenever she has more xylophones than yams, the slope is –1/2. Jane would be indifferent between a bundle with 24 xylophones and 36 yams and another bundle with 34 xylophones and (a) 28 yams. (b) 32 yams. (c) 22 yams. (d) 25 yams. (e) 26.50 yams.

4. Which of the following statements about demand-elasticity is correct? E (a) if demand is price-inelastic, an increase in price will lower total expenditures. (b) if demand is price-elastic, an increase in price will increase total expenditures . (c) if demand is price-elastic, an increase in price will leave total expenditures unchanged. (d) If demand is unit-elastic, a decrease in price will decrease total expenditures. (e) if demand is price-inelastic, a decrease in price will decrease total expenditures.

5. An individual considers goods X and Y to be perfect complements. Thus, D (a) the Hicksian demand curve for X is steeper than the Marshallian demand curve. (b) the Marshallian demand curve for X is steeper than the Hicksian demand curve. (c) the Marshallian and Hicksian demand curves are coincident. (d) the Hicksian demand curve is vertical. (e) None of the above. 3

Since the Hicksian demand curve indicates only substitution effects and there are no substitution effects for perfect complements, the Hicksian demand curve is vertical in this special case.

6. In the graph below, the shock is a decrease in the price of yams. E (a) Yams are a normal good and substitutes for Xeroxes. (b) Yams are an inferior good and substitutes for Xeroxes. (c) Yams are a Giffen good. (d) Yams are a normal good and complements for Xeroxes. (e) Yams are an inferior good and complements for Xeroxes.

Label the initial, intermediate, and final points “A”, “B”, and “C”, respectively. The move from B to C represents the income effect. Therefore, since YB > YC, yams are inferior – consumption of yams fell when income (purchasing power) rose. The answer is either (b) or (e). The question becomes, are yams and Xeroxes substitutes or complements? Because the demand for Xeroxes increased (XC > XA) when the price of yams decreased, they are complements. Answer = (e).

7. For a Cobb-Douglas utility function, YXYXU),( , D

(a) preferences are homothetic. (b) the share of income spent on good Y is unrelated to the price of good X. (c) the income-consumption curve is linear. (d) (a), (b), & (c) are true (e) only (a) & (b) are true

We have shown that C-D preferences are homothetic. We have shown that expenditure shares are constant for C-D preferences. (a) & (b) are true. For (c), X* = I/PX, and if I increases by t%, then so does X*. In other words, if an IC is tangent to the budget line at (x1, y1), then the IC which passes through (tx1, ty1) will be tangent to the “tI” budget line. That is the definition of an income-consumption curve.

Xeroxes Yams XA XC XB YB YC YA

A C 4

8. If, at a given consumption bundle on the budget line, the marginal utility C of yams is twice the marginal utility of xylophones, and the price of yams is one-third the price of xylophones, the utility-maximizing consumer should (a) make no change in her consumption bundle. (b) consume more xylophones and fewer yams. (c) consume more yams and fewer xylophones. (d) consume more yams and the same number of xylophones. (e) None of the above.

We are told that MUY = 2MUX and PY = 1/3PX. We know that at the optimal consumption bundle, YXYX