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Illustrate Euler’s theorem for the Cobb-Douglas production function
(11 (12 a3 f(xlyxz,xs)=/-'1xlJrzx3 A>0,a,->0Vi
defined on Riv and Z a; = l.
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- To produce the next popular toy, a company has to pay a factory $250, 000 to set up the production line. They also have to pay $25 per item for the raw materials and labor. Write function for the average cost to produce x items. Then describe what happens to the average cost as the factory produces a large number of toys.Consider the following graph of y = f(x). E D A Which of the following statements about the function f is true? Select one: O f has an endpoint at E and a y-intercept at B. O f has a global maximum at A and a global minimum at C. O f has a critical point at C and a global minimum at D. O f has a global minimum at A and a y-intercept at D.Answer with solution
- Does the output maximization level of input use exist for the following function? If yes, then what is the exact input-use level? y = x1 + 0.1x12 - 0.05x13 + x2 + 0.1x22 - 0.05x23handwrite it out and include graph pleaseA small company manufactures and sells fishing poles. The cost of manufacturing fishing poles can be modelled by the function c(x) = 7x + 3, where x is the number of batches (each containing 1000 poles) manufactured. Revenue is modelled by r(x) = x³ - 10x² + 20x. The company has enough workers to produce a maximum of 1200 fishing poles. a State the domain of both the cost and revenue functions. b Find the number of fishing poles that the company should manufacture in order to maximize its profits. The company introduces a new process which allows them to produce 6000 poles. c Find the number of poles that would cause the company to minimize profits (or maximizes losses). d By graphing the cost and revenue functions, find the number of poles which should be manufactured if the company is to just break even (that is, the production level at which the costs and revenues are equal). e It would not maximize the company's profits to produce as many poles as workers are capable of producing.…
