Suppose an individual has the following utility function: U(x, y) = −4(x − 5.5)^2 − 2(y − 3.5)^2

Further assume that the price of good x, px = $6, the price of good y, py = $8, and the individual has an income m = $65

a) Draw an indifference curve (one IC is enough) that represents this person’s preferences. Please label the graph properly including values for x and y.

b) Intuitively, and without formally solving, can you guess the maximized values x" and y" for the above utility function. Explain your answer.

c) Derive the optimal values x" and y" by formally solving the above utility function subject to the above constraint. You can use any of the utility maximization techniques we learned in class.

d) Compare your answers in parts b) and c). Based on the utility function that is given in this problem as well as the budget constraint, can you explain the differences between the answers you found in parts b) and c) (if any). Be as detailed as possible with your explanation.

Solve h(x) =l -2x l

Solve y = 2 (x + 4)2 - 3

Please explain for each of the above provide examples · write down five (5) points on the graph of each equation · For each of your equation, does the graph of each equation have any intercepts? · State the domain for each of your equations. Write them in interval notation. · State the range for each of your equations. Write them in interval notation. · State whether each of the equations is a function or not giving your reasons for the answer. · Select one of your graphs and assume it has been shifted three units upward and four units to the left. · Incorporate the following four math vocabulary words into your discussion. Use bold font to emphasize the words in your writing. Do not write definitions; use sentences describing the thought behind your math.

o Function

o Relation

o Vertical Line test

o Transformation

Problem 3 (4+2+2 marks). (a) Implement the following algorithm, which is given a duplicate-free array array as input, in C++. whatDoIDo (array): 1) Build a heap from array (using buildHeap as explained in class), where the heap starts at position array[0]. 2) Starting from j = size of array - 1, as long as j>0: i. Swap the entries array[0] and array[j]. ii. Percolate down array[0], but only within the subarray array[0..j-1]. iii. Decrement j by 1. Provide three input/output examples for duplicate-free arrays of size about 10. (b) What does whatDoIDo do? Explain your answer. (c) What is the worst-case running time of whatDoIDo, in dependence of the size N of the given array? Explain your answer

A fun size bag of M&Ms has 4 blue, 3 orange, 3 red, 2 green, 2 yellow, and 1 brown M&Ms. What is the probability of randomly selecting 5 M&Ms where 3 are blue and 2 are orange?

For the following reaction: NiO2(s) + 4 H+(aq) + 2 Ag(s) → Ni2+(aq) + 2 H2O(l) + 2 Ag+(aq) script E° = 2.48 V Calculate the pH of the solution if script E = 2.32 V and [Ag+] = [Ni2+] = 0.012 M. Use the Standard Reduction Table.

In each of Problems 16 through 25, find all eigenvalues and eigenvectors of the given matrix. 16) A= ( 1st row 5 −1 2nd row 3 1) 23) A= (1st row 3 2 2, 2nd row 1 4 1 , 3rd row -2 -4 -1)

Velocity field for this system is:

V=[X^2-(y*z^1/2/t)]i-[z*y^3+(x^1/3*z^2/t^1/2)j+[-x^1/3*t^2/z*y^1/2]k

find the components of acceleration for the system.

Below is collected data of the question "how many kisses have you eaten in the past day?"
This is between men and women.
The tables are these:
Male: 4, 2, 3, 1, 3, 2, 2, 0, 2, 0, 3, 1, 1, 2, 3, 5, 4  Female: 1, 2, 2, 1, 2, 4, 2, 1, 1, 3, 2, 1, 0, 1, 0, 0

Generate the experimental design using the appropriate methodology. What is the structure of the experiment?

What does the data analysis tell you?
Construct a 98% confidence interval.
Find the standard deviation.
Apply the appropriate analysis method or methods?
What type of hypothesis method will you use?
Calculate the alternate and null hypothesis and state the conclusion about who eats more kisses, men or woman.

Question 3 Using R for calculations

In a competitive company, the income levels of its employees are not standardised and are awarded on a case-by-case basis after negotiations between individual employees and the company directors. An industry body wants an analysis of employee income with respect to their relative rank in the company. A random sample of 184 individuals in the company were recruited and their relative Rank and Income values were anonymously recorded.

The data is available below. The variables are defined below.

Income - The yearly income of the employee.

Rank - The relative rank of the employee’s position at the company (1 being highest rank, 9 being lowest)

a. Fit a simple linear regression to the data with Income as the response variable and worker Rank as the predictor.

b. Using your analysis in a. or otherwise, explain why simple linear regression is inadequate to explain the structure in this dataset.

c. Fit a polynomial regression model to the data and select the best order polynomial to explain the data using the significance testing techniques discussed in lectures.

d. Predict the Income for a person planning to apply for a position at Rank 5 at one of these competitive companies in the near future

In C

1- Use nested for loops to create an addition lookup table. Fill in an array and print out the following table showing the sum of the row and column numbers 0-9.

0  1  2  3  4..   <- column numbers   

1  2  3  4  5..   

2  3  4  5  6..  <- These nos. = Row + Column   

3  4  5  6  7..  <- for example 7 = 3 + 4   

4  5  6  7  8.. 
...   

^Row numbers

2- use

A hexadecimal version 16x16 table 0-F. Use print specifier %x to print numbers in hex instead of decimal.