Provide sufficient questions to the attached questions.

3. (a) Below are a countour map of a function f and a curve with equation g(r, y) = 15. Estimate the maximum and minimum values of f subject to the constraint that g(r, y) = 15. Explain your reasoning. (ry) = 15 50 (3 marks] (b) Explain in your own words how the method of Lagrange multipliers works in finding the extreme values of /(r, y) subject to the constraint g(r, y) = k. (Note that in this question you are not asked to show what steps you would take to find the extreme values. You are instead expected to briefly explain the theory behind why it works). [2 marks] (c) Your ecommerce company regularly couriers rectangular packages overseas. The girth of a rectangular package is defined to be the perimeter of a cross section perpendicular to the length. You prefer to use CheapAsChips Couriers for your international deliveries, but they will only carry rectangular packages where the sum of length and girth is at most 150 cm. Find The dimensions of the nurl5. The National Center for Health Statistics published data on heights and weights. We obtained the following data from 10 randomly selected males 8 - 12 years of age. Height 69 71 70 67 75 66 73 71 68 65 Weight 151 159 160 153 198 126 174 185 143 175 If the researcher uses "Height" to predict "Weight" then the response variable is [2pts] b. Use your calculator to create a scatter plot. Copy the scatter plot below (draw it). Make sure to label the horizontal axis and vertical axis, and provide the minimum and maximum values (displayed on your graph on your calculator) on each axis. [4pts] . Is the association between the two variables positive or negative, or no association? (circle one) [2pts] d. Use your calculator to find the regression line (or line of best fit) and the correlation r. (Make sure something has a hat on it.} Regression Equation: [4 pts] Correlation r = [2 pts] e. Use the equation in d. to find the predicted weight for a man who is 69" tall. Show work and box final answer. [3pts] f. Compute the residual associated with the man who is 69" tall. Show work and box final answer. [2pts] g. Identify the slope of the regression line:_ . Interpret it using the context of the problem. (Write a sentence and mention both men's heights and weights.) [3pts]2. Consider a. competitive economy with two goods, 9: and 3;. There are a continuum of identical consumers with measure 1. Each consumer has initial endowments w = (Um my), where mm > 0 and my = 0. The consumer's utility function is given by: U = (11110:; + (1 (1)1110!\" where Cm (Cy) is consumption of good 1: (good 3;) and 0