X value is equal to 0.263 and the Y value is 0.022

(b) Minimizing Average Cost BoxCo's main costs for producing each container are (1) the costs of the sheet metal and (2) the costs to weld the edges. Assume that the sheet metal can folded and that no welding is required to reinforce the folded edges. Suppose that it costs BoxCo F(X) dollars to make X square metres of sheet metal and G(Y) dollars to weld a length of Y metres, in a week. These functions are given below: 1 F(X) 330 (X - 80)* + 1500 G(Y) = 5Y 1. Assume that each container will have a surface area of 1 m and that BoxCo will follow your pod's advice in part (a) by using your recommended dimensions in order to maksimize the volume of each container. What is the total cost for producing , containers? (Be sure to include both the cost of the sheet metal and the cost of the welding.) Find a formula for this cost function. ii. Prepare to Graph: In the next step, you will use a computer to make a graph of the cost function. However, it is important to choose the viewing window in such a way so that we can see all of the important behaviour, including critical points and inflection points. Use your formula for the cost function to find the critical points and inflection points, then choose an appropriate viewing window so that these points are appropriately centred. iii. Graph: Use a computer to make a graph of the cost function, with the viewing window you determined in part (ii). Be sure that the axes are labelled appropriately, including units. iv. Use the graph of the cost function to determine approximately how many containers should be produced in order to minimize the average cost per container. Explain your reasoning and sketch a picture to accompany your explanation. v. Use a graph of the average cost function to roughly confirm your answer. (b) Minimizing Average Cost BoxCo's main costs for producing each container are (1) the costs of the sheet metal and (2) the costs to weld the edges. Assume that the sheet metal can folded and that no welding is required to reinforce the folded edges. Suppose that it costs BoxCo F(X) dollars to make X square metres of sheet metal and G(Y) dollars to weld a length of Y metres, in a week. These functions are given below: 1 F(X) 330 (X - 80)* + 1500 G(Y) = 5Y 1. Assume that each container will have a surface area of 1 m and that BoxCo will follow your pod's advice in part (a) by using your recommended dimensions in order to maksimize the volume of each container. What is the total cost for producing , containers? (Be sure to include both the cost of the sheet metal and the cost of the welding.) Find a formula for this cost function. ii. Prepare to Graph: In the next step, you will use a computer to make a graph of the cost function. However, it is important to choose the viewing window in such a way so that we can see all of the important behaviour, including critical points and inflection points. Use your formula for the cost function to find the critical points and inflection points, then choose an appropriate viewing window so that these points are appropriately centred. iii. Graph: Use a computer to make a graph of the cost function, with the viewing window you determined in part (ii). Be sure that the axes are labelled appropriately, including units. iv. Use the graph of the cost function to determine approximately how many containers should be produced in order to minimize the average cost per container. Explain your reasoning and sketch a picture to accompany your explanation. v. Use a graph of the average cost function to roughly confirm your