1. Find the critical point of the function f(x, y)=8x+8xy+12x+10y+10y+6 and classify it. 2 2. A...

  

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1. Find the critical point of the function f(x, y)=8x+8xy+12x+10y+10y+6 and classify it. 2 2. A consumer has utility function u(x,,x,)=x,x,' for two goods, X, and X,. (Here x, and x, are respectively, the quantities of good X, and X,.) Suppose that each unit of good X, costs $1 and each unit of good X, costs S2, and that the consumer has an amount of $100 to spend on these two goods. By using the Lagrange multiplier method, determine the quantities (x, and x,) of good X, and X, that maximize the consumer's utility. [10 marks] 3. Express the following system of equations in matrix form and solve it using a matrix method. x-y+z=2 3x+y-2z=0 5x-2y-z=1 [5 marks] 1. Find the critical point of the function f(x, y)=8x+8xy+12x+10y+10y+6 and classify it. 2 2. A consumer has utility function u(x,,x,)=x,x,' for two goods, X, and X,. (Here x, and x, are respectively, the quantities of good X, and X,.) Suppose that each unit of good X, costs $1 and each unit of good X, costs S2, and that the consumer has an amount of $100 to spend on these two goods. By using the Lagrange multiplier method, determine the quantities (x, and x,) of good X, and X, that maximize the consumer's utility. [10 marks] 3. Express the following system of equations in matrix form and solve it using a matrix method. x-y+z=2 3x+y-2z=0 5x-2y-z=1 [5 marks]