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# P14 - given by C x = √ x 2 x 8 and d x = √ 22 6 x x...

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Project 13/14 MAC 2233 1. An underwater pipe begins to leak oil that spreads outward in the shape of an expanding sphere. Recall that the volume of a sphere is V = 4 3 πr 3 , where r is the length of its radius. Suppose the company that owns the pipe takes some measurements and discovers that the radius (in square feet) of the spill has been r ( t ) = 3 + 2 t + t 2 , where t is the number of hours since the spill began ( t = 0 ). Calculate dV dr and calculate dr dt . What are the radius and volume of the spill after 1 hour? 4 hours? What are the values of dV dr and dr dt after 1 hour? 4 hours? What is the value of dV dt after 1 hour? 4 hours? What do these numbers represent? 2. Suppose the cost and demand functions for a product manufactured by a certain company are
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Unformatted text preview: given by C ( x ) = √ x 2 + x + 8 and d ( x ) = √ 22 + 6 x x where x is in thousands, d is in dollars, and C is in thousands of dollars. Write a formula for the proﬁt function P ( x ) . What production level x = Q will result in breaking even? Calculate the marginal proﬁt function, and evaluate it when the production level is x = Q ( Q thousand units). Interpret the result. Use the derivative and a calculator to approximate the marginal proﬁt at production level x = 1 and when x = 3 . Should the company increase or decrease production at each level?...
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