16) The cost in dollars, of producing x units is given by the function $C(x) = 3500 + 5x - 0.04x^2 + 0.003x^3$ a) Find the average cost and marginal cost functions. $AC = frac{C}{x} = frac{3500}{x} + 5 - 0.04x + 0.003x^2$ $C'(x) = 5 - 0.08x + 0.009x^2$ b) Find the minimum average cost and the production level that will minimize the average cost. $AC' = frac{-3500}{x^2} - 0.04 + 0.006x = 0$ $-3500 - 0.04x^2 + 0.006x^3 = 0$
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The cost function is given by: C(x) = 3500 + 5x - 0.04x^2 + 0.003x^3 a) Show more…
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(a) 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 $. Show that if the average cost is a minimum, then the marginal cost equals the average cost. (b) If $ C(x) = 16,000 + 200x + 4x^{3/2} $, in dollars, find (i) the cost, average costs, and marginal costs at a production level of $ 1000 $ units; (ii) the production leve that will minimize the average cost; and (iii) the minimum average cost.
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(a) If $C(x)$ is the cost of producing $x$ units of a commodity, then the average cost per unit is $c(x)=C(x) / x .$ Show that if the average cost is a minimum, then the marginal cost equals the average cost. (b) If $C(x)=16,000+200 x+4 x^{3 / 2},$ in dollars, find (i) the cost, average cost, and marginal cost at a production level of 1000 units; (ii) the production level that will minimize the average cost; and (iii) the minimum average cost.
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