Question 1 A company is the only producer of two goods, X and Y. When the prices for X and Y are px and py per unit (respectively), consumers will purchase quantities x and y (respectively) according to the demand equations pX+pY = 544x4y and pXpy=222x+2y If the company's joint total cost lnction (that is, the cost of producing quantities x ofXand y on) is TC(x, y) = 10 + 2x2 39:31 + 2y2, nd their prot function,1r(x, y). Hence determine the quantities x and y that maximise this prot. (10 marks) Question 2 The weekly output (in units) of a factory depends on the amount of capital and labour it employs as follows: if it uses k units of capital and l of labour then its output is Q(k,l) = Ji units. The cost to the rm of each unit of capital is 1 dollars, and the cost of each unit of labour is 4 dollar. Use the method of Lagrange multipliers to nd the minimum weekly cost of producing a quantity of 400 units. (10 marks)