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Numerade Educator



Problem 71 Hard Difficulty

A company estimates that the marginal cost (in dollars per item) of producing $ x $ items is $ 1.92 - 0.002x $. If the cost of producing one item is $ \$562 $, find the cost of producing 100 items.


it costs $\$ 742.08$ to produce 100 items


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Video Transcript

Hello. You have a question in which we have been given the marginal cost of producing X items. Okay so if C. X. Or C. Is the cost and access the number of attempt then marginal cost will be equal to Uh huh. D. c. by D. X. This is being given as 1.9 to 0 002 x. So It is given that if the cost of producing one item is 562. So we have to find the cost of producing 100 items. Okay so let us right and says the sequel to 1.9: -0.002 x. Dx. Let us integrated and will be calculating just like this that if the cost of producing one item in 562 so we have to find cost of producing 100. Oh okay I do. Uh So let us just first. All right. It's like if item is Cause probably one item if item is when then cost is $562. And when item is 100. So we have to find the cost. Let us say yeah. Tradition C -562 Will be called to 1.92 x -0.02 Access Choir by two. And this is 12 100. So this is uh 1.92 x minus 0.01 Excess Square 12. 100. Okay now Let us start plugging in the limits. 1.92. Upper LTD 100 Lower LTD one -0.01 upper limit is 100 Whole Square -1 Whole Square. So this is 1.92, 1.92 and two 99 -0.01 into 10,000 -1, 9900 and 99. Yeah. 1.92 In 299 minus 101 9999. Okay, So this becomes 90 points 09 C -562. So total cost, it could be 90, 9th place 562. Mhm. Yeah. Yes. Rules 562. We should add. So the cost of producing 100 items, $652.09. Okay, thank you.