Pipe is to be laid from point A in a rectangular plot of size 10 x 20 feet to a point P on side BC and from there on to C as shown in red in the figure below. The cost of laying pipe within the plot is $c per foot (it must be underground), while the cost of laying pipe along the side of the plot is $d per foot. 10 20 (a) Determine the total cost, f(x), as a function of c, d and x, where x is the distance from P to B. (Note that f(x) is discontinuous at x = 0.) f(x) = dollars (b) What is the cost of laying the pipe on the side of the plot (x = 0) when c = 30 and d = 25? (Round your answer to the nearest cent.) $ (c) What is the least cost of laying the pipe when c = 30 and d = 25? (Round your answer to the nearest cent.)

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Domain

In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.