Suppose the dollar cost of producing x video cameras is $C(x) = 500x - 0.003x^2 + 10^{-8}x^3$. Estimate the marginal cost at the production level $x = 5500$. (Use decimal notation. Give your answer to three decimal places.) 467.908 The estimated marginal cost is $ Correct Answer Find the actual cost $C(5501) - C(5500)$. (Use decimal notation. Give your answer to three decimal places.) 467.908 The actual cost is $ Incorrect Answer Find the average cost per camera at production level $x = 5500$. (Use decimal notation. Give your answer to three decimal places.)
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Suppose that for $x \geq 1000$, the dollar cost of producing $x$ video cameras is $C(x)=500 x-0.003 x^{2}+10^{-8} x^{3}$. (a) Estimate the marginal cost at production level $x=5000$ and compare it with the actual cost $C(5001)-C(5000)$. (b) Compare the marginal cost at $x=5000$ with the average cost per camera, defined as $C(x) / x$.
Differentiation
Rates of Change
In Exercises $39-46,$ use $E q .(3)$ to estimate the unit change. Suppose the dollar cost of producing $x$ video cameras is $C(x)=$ $500 x-0.003 x^{2}+10^{-8} x^{3}$ (a) Estimate the marginal cost at production level $x=5000$ and compare it with the actual cost $C(5001)-C(5000) .$ (b) Compare the marginal cost at $x=5000$ with the average cost per camera, defined as $C(x) / x .$
DIFFERENTIATION
If C(x) is the cost of producing x units of a commodity, then the average cost per unit is c(x) = C(x)/x. Consider the cost function C(x) given below. C(x) = 3,000 + 210x + 6x^3/2 (a) Find the total cost at a production level of 1000 units. (Round your answer to the nearest cent.) $ 402736.7 (b) Find the average cost at a production level of 1000 units. (Round your answer to the nearest cent.) $ 402.7 per unit (c) Find the marginal cost at a production level of 1000 units. (Round your answer to the nearest cent.) $ 494.6 per unit (d) Find the production level that will minimize the average cost. (Round your answer to the nearest whole number.) 10.1 units (e) What is the minimum average cost? (Round your answer to the nearest dollar.) $ 5313 per unit
Eduard S.
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