3. Derive the profit function (p) and supply function (or correspondence) y(p) for the single- output technologies whose production functions f (2) are given by (a) f(2)=√√√₁ +37₂ (b) f(2)=√min{21,322} (c) f(z) = (z + 325)¹/P, for p<1
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- i need M,N,O subparts solution of this question2) The owner of a restaurant that you are thinking of purchasing, tells you for x customers per week the weekly cost and revenue in dollars is C(x) = 15000+2x and R(x) = 500x-3x² a) Find the profit function P(x) b) Find the break-even quantities rounding properly to a whole number. (Hint: Use the Quadratic formula) c) Why is the minimum break-even quantity important?Just part (d) and (e)
- i need j,k,l subpartsQuestion 5 > A firm manufactures a commodity at two different factories, Factory X and Factory Y. The total cost (in dollars) of manufacturing depends on the quantities, and y produced at each factory, respectively, and is expressed by the joint cost function: C(x, y) = x² + xy + 2y² + 200 A) If the company's objective is to produce 600 units per month while minimizing the total monthly cost of production, how many units should be produced at each factory? (Round your answer to whole units, i.e. no decimal places.) To minimize costs, the company should produce: units at Factory X and units at Factory Y B) For this combination of units, their minimal costs will be enter any commas in your answer.) Question Help: Video Submit Question dollars. (Do notf(k,l) = 1/3k1/3, the A firm is faced with a production technology that uses capital and labor: q = price of labor is w, and the price of capital is r. (a) Write down the cost minimization problem and determine the contingent input demand functions: 1(w, r, q) and k°(w, r, q). Also, derive the cost function C(w, r,q). (b) The firm operates in a perfectly-competitive market and faces a market price of p. Write down the firm's profit function. Solve the maximization problem to determine (1) input demand, that is, the demand for labor and capital as a function of w, r, and p (2) the output supply function, q as a function of w, r, and p.
- The Brain Bucket Company (BBC) produces helmets for winter sports. It has production facilities in Toronto and Winnipeg. The production function for the Toronto facility is Qr LT, (1) where LT is the quantity of labour hired in Toronto. The production function for the Winnipeg facility is VLw. (2) Qw where Lw is the quantity of labour hired in Winnipeg. The wage rate in Winnipeg is one and the wage rate in Toronto is two. Answer the following: (a) If BBC wishes to produce Q helmets at the lowest possible cost, how should it distribute production between the two cities? Use your answer to find a function showing the cost of producing Q helmets.Let R(x), C(x), and P(x) be, respectively, the revenue, cost, and profit, in dollars, from the production and sale of x items. If R(x) = 4x and C(x)=0.003x² + 1.6x + 50, find each of the following a) P(x) b) R(150), C(150), and P(150) c) R'(x), C'(x), and P'(x) d) R'(150), C'(150), and P'(150) a) P(x) = (Use integers or decimals for any numbers in the expression.) b) R(150)=$ (Type an integer or a decimal.) C(150)=$ (Type an integer or a decimal) *** P(150) $ (Type an integer or a decimal.) c) R'(x) = (Type an integer or a decimal) C'(x)= (Use integers or decimals for any numbers in the expression) P'(x)= (Use integers or decimals for any numbers in the expression)The price-demand equation and the cost function for the production of table saws are given, respectively, by x 12,000 - 40p and C(x) = 98,000 + 70x, where x is the number of saws that can be sold at a price of Sp per saw and C(x) is the total cost (in dollars) of producing x saws. Complete parts (A) through (H) below. (A) Express the price p as a function of the demand x. (x-12000) The price function is p= -40 (B) Find the marginal cost. The marginal cost is 70 (C) Find the revenue function. (x-12000) The revenue function is R(x) = -40 (D) Find the marginal revenue. (12000-x) The marginal revenue is 40 (E) Find R'(1.500) and R'(4.500) and interpret these quantities. Find and interpret R' (1.500). Select the correct choice below and fill in the answer boxes within your choice. (Simplify your answers) A. R'(1.500) = 287 5 at a revenue of S per saw, saw production is increasing at the rate of per dollar.
- Hi, Please help. Thank you. PLEASE SUBMIT AN IMAGE OF THE REQUESTED ILLUSTRATION DISCUSSED BELOW. (PLEASE MAKE SURE YOU LABEL ALL APPROPRIATE COMPONENTS AND USE THE CORRECT NUMERICAL SCALES FOR YOUR GRAPH). HANDWRITTEN/HANDDRAWN GRAPHS ONLY, Please. Using the data presented from the table you need to fill out below, please GRAPH AND LABEL the ATC, AVC, AFC, MC, d, and MR functions represented by this data, assuming the market price of this product is $150.00 per unit.TC(Q)=5+2* Q² Provide a table of the marginal costs and average total costs for Q = 0, 1, 2, ..., 10. At what quantity are economies of scale exhausted? If the good/service being sold has a constant price of $20, at what quantity are profits maximized? (Note: If there is not a quantity integer that corresponds to the profit-max condition, firms would halt production at the last unit producing profit.)Suppose a company's revenue function is given by q³+370q² and its cost function is given 2 R(q) by C(q) = 380 + 12q, where q is hundreds of units sold/produced, while R(q) and C(q) are in total dollars of revenue and cost, respectively. = A) Find a simplified expression for the marginal profit function. (Be sure to use the proper variable in your answer.) MP(q) = = B) How many items (in hundreds) need to be sold to maximize profits? Answer: hundred units must be sold. (Round to two decimal places.)