1. An oil refinery is located on the north bank of a straight river that is 2 km wide. A pipeline is to be constructed from the refinery to storage tanks located on the south bank of the river 10 km east of the refinery. The cost of laying pipe is $400,000/km over land to a point P on the north bank and $800,000/km under the river to the tanks. To minimize the cost of the pipeline, how far (in km) from the refinery should P be located? (Round your answer to two decimal places.) 2. The illumination of an object by a light source is directly proportional to the strength of the source and inversely proportional to the square of the distance from the source. If two light sources, one two times as strong as the other, are placed 12 ft apart, how far away (in ft) from the stronger light source should an object be placed on the line between the two sources so as to receive the least illumination? (Round your answer to two decimal places.)

3. A baseball team plays in a stadium that holds 55,000 spectators. With ticket prices at $10, the average attendance had been 49,000. When ticket prices were lowered to $8, the average attendance rose to 51,000. a. Find the demand function (price p as a function of attendance x), assuming it to be linear. b. How should ticket prices be set to maximize revenue? (Round your answer to the nearest cent.)

4. The upper right-hand corner of a piece of paper, 6 inches by 4 inches, is folded over to the bottom edge as shown in the figure. How would you fold the paper so as to minimize the length of the fold? In other words, how would you choose x (in inches) to minimize y?