A worker is to construct an open rectangular box with a square base and a volume of 147 ft3. If material for the bottom costs​ $6/ft2 and material for the sides costs ​$7​/ft2 what dimensions will result in the least expensive​ box? What is the minimum​ cost? Let x be the length of one side of the base of the box. Express the total cost of the​ materials, C, in terms of x. Find C(x)

Consider the following problem: A farmer has 3600 ft of fencing and wants to fence off a rectangular field that borders a straight river. He does not need a fence along the river (see the figure). What are the dimensions of the field of largest area that he can fence? (Let x be the width of the field in feet and l be the length of the field in feet.) (a) Experiment with the problem by drawing several diagrams illustrating the situation. Calculate the area of each configuration, and use your results to estimate the dimensions of the largest possible field. (Round your answers to the nearest hundred feet.) (b) Find a function that models the area of the field in terms of one of its sides (c) Use your model to solve the problem, and compare with your answer to part (a)

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