A rational consumer's utility for consuming goods X and Y is expressed by the following function:

QUESTION 1 (22 Marks) QUESTION 3 (6 Mar A firm's total cost fu A rational consumer's utility for consuming goods X and Y is expressed by the following function: U = 2x - 4y + 20 a) Write an e Where U is Total Utility; x is the quantity of good X that are consumed; and y is the quantity of good Y that are consumed. Suppose the consumer spends all his income, of N$1000, on goods X and Y, and the prevailing prices for good X and Y, are N$8 per unit and N$10 per unit, respectively. Draw HERESS the consumer's budget constraint. N b) Given the function and the additional information in part (a), determine the optimal consumption bundle for this consumer? c) Use an indifference curve and a budget constraint to show this consumer's optimal NB Please name consumption bundle in a graph? 1.2 Suppose Natasha is a rational consumer and her Total Utility (TU) function for beef and mutton is represented by the following equation: U = 48x - 2X'+ 54y- 3y Where U represent Natasha's Total Utility function for beef and mutton; and x and y are the quantities (in kilograms) of beef and mutton consumed, respectively. a) The prevailing prices of beef and mutton are N$45/kilogram and N$65/kilogram, and Natasha's budget for beef and mutton is N$600. Given this information, determine the quantities of beef and mutton in Natasha's optimal consumption bundle. b) Given the information in part (a) draw a diagram to show Natasha's optimal consumption 1000 bundle using an indifference curve and a budget constraint