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The marginal cost is equal to C'(x), and fixed costs are being disregarded in this problem. So we know that the marginal cost is equal to the function that is given. The value for x is the number of pounds (lbs) of coffee being roasted. With this in mind, HOWEVER many pounds of coffee being roasted will automatically become the value for x. In the function you can see where it says x is less than or equal to 200 (lbs of coffee)...disregard this note because the word problem literally tells us what the value for x is. X being less than or equal to 200 lbs of coffee is an approximation. This problem doesn't have an approximate value because it literally says 150 lbs of coffee. So, if x equals lbs of coffee, input x (which is 150 lbs of coffee) into the function. The function should now say C'(150) = -0.027(150) + 6.25. Do the algebra from there and your answer should be 2.2. Keep in mind that this means $2.20, so when it says round to the nearest cent, you do not have to round this answer. Hope I helped!
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Dec 4th, 2015
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