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 $52 per mile to lay, the second section runs from point Q to point R and costs $40 per mile, the third runs from point R to point S and costs $38 per 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. Please show your answers to 4 decimal places. 2 Miles 1 Mile R 30 10 miles 50 Find the point on the line 4x + 6y +7=0 which is closest to the point (5,-3). Please enter exact answers in whole numbers or factions. 56 3,- 105 26 X You need to construct an open-top rectangular box with a square base that must hold a volume of exactly 625 cm. The material for the base of the box costs 5 cents/cm and the material for the sides of the box costs 3 cents/cm. Find the dimensions for a box that will minimize the cost of the materials used to construct box. Please show your answers to at least 4 decimal places. width: 5.3861 height: 10.7721 X cm X cm Suppose that one factory inputs its goods from two different plants, A and B, with different costs, 3 and 9 each respective. And suppose the price function in the market is decided as p(x, y) = 100 - x - y where x and y are the demand functions and 0 x, y. Then as X = y = the factory can attain the maximum profit, 200 X Suppose that one factory inputs its goods from two different plants, A and B, with different costs, 2 and 9 each respective. And suppose the price function in the market is decided as p(x, y) = 100 - x - y where x and y are the demand functions and 0 x, y 30. Then as x = y = the factory attains the maximum profit, 1043.856 X