QUESTION 20 [CLO-5] C(x) is the total cost of producing x units of a particular commodity. Assume C(x) is in dollars. Use marginal cost to estimate the cost of producing the 21st unit. What is the actual cost of producing the 21st unit? C(x) = 1/4 x^2 + 4x + 65 estimated cost = $14.00; actual cost = $13.75 estimated cost = $13.75; actual cost = $14.00 estimated cost = $14.00; actual cost = $14.25 estimated cost = $14.25; actual cost = $14.00
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Step 1: Calculate the marginal cost function: Given C(x) = x^2 + 4x + 65, find C'(x) = 2x + 4. 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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