4.3

1. Find the critical point of the function f(x,y)=53x+7x²2yy²

2. An open-top rectangular box is being constructed to hold a volume of 150 in³. The base of the box is made from a material costing 6 cents/in². The front of the box must be decorated, and will cost 9 cents/in². The remainder of the sides will cost 4 cents/in². Find the dimensions that will minimize the cost of constructing this box. Front width: in. Depth: in. Height:

3. An engineer is designing a pipeline which is supposed to connect two points P and S. The engineer decides to do it in three sections. The first section runs from point P to point Q, and costs $50 a mile to lay, the second section runs from point Q to point R and costs $56 mile , the third runs from point R to point S and costs $46 a mile. Looking at the diagram below, you see that if you know the lengths marked x and y, then you know the positions of Q and R. Find the values of x and y which minimize the cost of the pipeline. x =miles y =miles