A business owner needs to run a gas line from his business to a gas main...

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A business owner needs to run a gas line from his business to agas main as shown in the accompanying diagram. The main is 30-ftdown the 12-ft wide driveway and on the opposite side. A plumbercharges $4 per foot alongside the driveway and $5 per foot forunderneath the driveway.
a) What will be the cost if the plumber runs the gas lineentirely under the driveway along the diagonal of the 30-ft by12-ft rectangle? b) What will be the cost if the plumber runs thegas line 30-ft alongside the driveway and then 12-ft straightacross? c) The plumber claims that he can do the job for $160 bygoing alongside the driveway for some distance and then going underthe drive diagonally to the terminal. Find x, the distancealongside the driveway. d) Write the cost as a function of x andsketch the graph of the function. e) Use the minimum feature of agraphing calculator to find the approximate value for x that willminimize the cost. f) What is the minimum cost (to the nearestcent) for which the job can be done?

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4.3 Ratings (594 Votes)

a As per the Pythagoras theorem if the diagonal of therectangle is d ft then d2 302122 900144 1044 so that d 1044 3231 ftapproximately on rounding off to 2 decimal places Thus if theplumber runs the gas line entirely under the driveway along thediagonal then the cost See Answer

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