1. The cost of fuel per kilometer for a truck travelling v kilometers per hour is given by the equation C(V) = - 50 150 a. What speed will result in the lowest fuel cost per kilometer? Hint, you should test the point to ensure that it is a minimum. b. Assume the driver is paid $53/h. What speed would give the lowest cost, including fuel and wages, for a 1 000 km trip? 2. A lifeguard at a public beach has 600 m of rope available to lay out a rectangular restricted swimming area using the straight shoreline as one side of the rectangle. a. If she wants to maximize the swimming area, what will the dimensions of the rectangle be? To ensure the safety of swimmers, she decides that nobody should be more than 55 m from the shore. What should the dimensions of the swimming area be with this added restriction? 3. A soup can of volume 625 m' is to be constructed. The material for the top costs 0.4 c/cm while the material for the bottom and sides costs 0.25 c/cm2. Find the dimensions that will minimize the cost of producing the can. 4. Two pens, with one common side are to be built with 75 m of fencing. Both pens are to be rectangles (both the same side lengths). Find the dimensions that maximize the total area. 5. While walking home, you notice that you still need to travel 7 km east then 3 km south. Wanting to get home as quickly as possible, you realize that part way into the 7 km walk, you can cut across a field to for a more direct route home. You decide to run part of the way, with a speed of 6.5 m/s then walk the rest of the way at a speed of 3.4 m/s. How far along the 7 km distance should you run before turning to cut through the field so you reach home as quickly as possible? you 7 km run walk 1 3 km home Calculus and Vectors Lesson 12 6. A box with an open top is to be constructed from a square piece of cardboard, 6 m wide, by cutting out a square from each of the four corners and bending up the sides. Find the largest volume that this box can have