A cost of production function is given as C (n) = (n – 100)2 + 100 where C (n) is the cost in $ of producing n number of a certain product. Use the derivative to determine the n which will minimize the cost of production. n = 10 n = 100 c) n = 50 d) n = 20
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A cost of production function is given as
C (n) = (n – 100)2 + 100
where C (n) is the cost in $ of producing n number of a certain product.
Use the derivative to determine the n which will minimize the cost of production.
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- The total cost (in hundreds of dollars) of producing x calculators per day is given by the equation. 20- 15- 10- C(x) = 6 + /2x + 32 Osx< 50 Perform the following calculations and interpret the results. 10 20 30 40 50 Production C'(x) =U %D Cost (hundred dollars)Assume that it costs a company approximately C(x) = 400,000 + 140x + 0.003x? dollars to manufacture x smartphones in an hour. (a) Find the marginal cost function. 400,000 – 0.000009 Use it to estimate how fast the cost is increasing when x = 10,000. 2$ per smartphone Compare this with the exact cost of producing the 10,001st smartphone. The cost is increasing at a rate of $ per smartphone. The exact cost of producing the 10,001st smartphone is $ Thus, there is a difference of $ (b) Find the average cost function C and the average cost to produce the first 10,000 smartphones. C(x) = C(10,000) = $ (c) Using your answers to parts (a) and (b), determine whether the average cost is rising or falling at a production level of 10,000 smartphones. -Select--- at a production level of 10,000 smartphones. The marginal cost from (a) is --Select--- than the average cost from (b). This means that the average cost isWhenever postage rates change, some newspaper publishes a graph such as the one shown below, which shows the price of a first-class stamp from 2006 to 2016. Cost(dollam) 0.85- 0.70- 0.55 0.40 0.25 of 2006 2008 Price of a First-Class Stamp [Select] 2010 Year 2012 2014 2016 (a) Let f be the function whose rule is f(x) = cost of a first-class stamp in year x. Find f(2012) and f(2015). f(2012) = [Select] f(2015): =
- It costs a company $58 to produce 6 units of a product and $78 to produce 10 units. Assuming that the cost is linear, how much does it cost to produce 25 units?The at a given production level x approximates the cost of producing the (x + 1)st or next item. screenshot attached(a) In the implicit function exy² + x² = 1, y is a function of x. Find an explicit formula for y' and evaluate it at (x, y) = (0,0).
- A cost function is given. C(q) = 3600 + 5q-0.02q² + 0.00039³ (a) Find the average cost and marginal cost functions. +5 -0.02q +0.0003q average cost 3600 9 marginal cost 5 -0.04q+0.0009q (b) Use graphs of the functions in part (a) to estimate the production level that minimizes the average cost. (Round your answer to the nearest integer.) 194 ✓ units (c) Use calculus to find the minimum average cost. (Round your answer to two decimal places.) $ 32.41 X (d) Find the minimum value of the marginal cost. (Round your answer to two decimal places.) $ 4.56What is the formulae used to find unit cost?(i) Find the rate of change of the function f(x) =x + 2/ 1 − 8x with respect to x when x = 1.(ii) The number of units Q of a particular commodity that will be produced with Kthousand dollars of capital expenditure is modeled by Q(K) = 500 K2/3Suppose that capital expenditure varies with time in such a way that t months from nowthere will be K(t) thousand dollars of capital expenditure, whereK(t) =2t4 + 3t + 149 / t + 2 (a) What will be the capital expenditure 3 months from now? How many units will be producedat this time?(b) At what rate will production be changing with respect to time 5 months from now?Will production be increasing or decreasing at this time?
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