A firm produces its output using the following production function: filters] = 1,3111 #14412 where x. denotes the amount of factor'l and x; denotes the amount of factor 2. The market price of factor 1 is $4, and the market price of factor 2 Is $10. {a} To produce y = 3 units of output with the lowest cost: how much factor 1 and factor 2 shoutcl the firm use? Find the optimal trundle of inputs and calculate the minimal cost. {in} Now, suppose the price of factor 2 has increased to $40, and the price of factort is still $4. To produce 1; = 1 unit of output with the lowest costu how much of tactor 1 and factor 2 should the firm use? Find the optimal bundle of inputs and calculate the minimal cost. tc} Suppose the firm utilizes a new technology to produce output. According to the new production function. factors: and 2 must be combined in fixed proportions. To produce 2 units of output. the firm needs to combine 3 units of factor 1 with %e unit of factor 2. If the price of factor 1 is $2 a unit and the price of factor 2 is $4 a unit, drew an isocost representing the lowest cost of producing 2 units of output.