Given the utility function U = x/²x/2 find a general expression for MRCS in terms of x₁ and x₂.

On a given evening, J. P. enjoys the consumption of cigars (c) and brandy (b) according tothe functionU(c, b) = 20c− c²+ 18b − 3b²a. How many cigars and glasses of brandy does he consume during an evening? (Cost isno object to J. P.)b. Lately, however, J. P. has been advised by his doctors that he should limit the sum ofglasses of brandy and cigars consumed to 5. How many glasses of brandy and cigarswill he consume under these circumstances?

(b) It is thought that a consumer measures the utility, u(x, y), of possessing a quantity, z, of apples and a quantity, y, of oranges by the formula u(x, y) = rªyla, where a is a constant. Suppose that apples cost p dollars each and oranges q dollars each. If the consumer has M dollars to spend on apples and oranges, use the method of Lagrange multipliers to find the quantity of each that he will buy in terms of a, p, q and M. [You are not required to justify the use of the method of Lagrange multipliers here.] For equally priced apples and oranges when he has one dollar to spend, he is actually observed buying one apple and two oranges. What value of a does this imply?

4. Find the maximum values of the following functions and show whether they are maximized at their maximum values. (a) y= f(x)=10x – x² (b) z=10x+10y-xy-x² - y²

Eren’s two main hobbies are taking vacations overseas (V) and eating expensive meals (M). His utility function is given as: U(V,M) = V^2MLast year, the average price of taking a vacation overseas was US$200 and the average price of an expensive meal is $50. However, due to supply problems in Onions, the average price of an expensive meal rose to $75. The average price of a vacation did not change. His income, which is $1500, did not change.  Suppose that the Department of Welfare wants to know how much should be given to Eren to offset his change un utility due to the price increase of an expensive meal. Calculate the compensative variation (CV).

80 60 40 20 0 a N b A 10 a Multiple Choice 20 B 30 C 40 b C NE 50 60 Refer to the diagram. The slope of curve ZZ at point A is approximately

Find positive numbers x and y such that x + y = 72 and 6xy² is maximized.

Brit-Brick is a company that produces bricks and cement in the UK. Their largest consumer is ConstrUK, a UK construction company. The manager of Brit-Brick has asked the research department to find out how sensitive ConstrUK's demand for bricks is. The research department has estimated that ConstrUK's preferences over bricks (x) and cement (y) can be described by the utility function wwwww U(x,y) xb/10 y1-b/10 , where b=8, and where x and y are measured in bags. Example: if b=4, then U(x,y) x*/10 yl-4/10 = x²/5 y3/5. %3D The price for one bag of cement is equal to £1. It is estimated that ConstrUK's budget is £10,000. Find the price-consumption curve for bricks and the corresponding demand curve.

Upon graduating from UT this May, you take on a management position working at UtMax theater. You will consider the utility of seeing performance over 1 month, and suppose that at a regular price of $$$ per ticket (my assigned ticket price is 145), customers will see no performance, however with the price reduced by $5, customers will see one performance per month and when reduced by $10, customers will see two performances. As long as the number performances, x, is small, your demand function for performance can be modeled by p=D(x). Write down your demand function.

Exercise A1 Name three kinds of graphs and briefly state when is most appropriate to use each type of graph.