a) A profit maximising firm has a marginal cost function given by MC = 6Q2-10Q+12 and a marginal revenue function given by MR = 100-2Q. i) Find expressions for the firm's Total Revenue and Total Cost functions in terms of Q. ii) Find the profit maximising level of output if the firm's fixed costs
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- The total revenue curve of a firm is R(q) = 40q − 12q2 and its average cost A(q) =1/30q2 − 12.85q + 20 +400/q, where q is the firms output. Is the rate of change of profit increasing or decreasing when the ouput level of the firm is 10 units? Determine the level of output for which the firms profit is maximized. What is the firm's maximum profit?A firm faces the following average revenue (demand) curve: P = 100 - 0.01Q. where Q is weekly production and P is price, measured in cents per unit. The firm’s cost function is given by C = 5Q +2000. Assuming the firm maximizes profits production, determine the price and total profitper week.The total revenue curve of a firm is R(q) = 40q − 12q2 and its average cost A(q) = 1/30 q2 − 12.85q + 20 + 400/q , ,where q is the firms output. Derive expressions for the firm's: (i) total cost function (ii) total profit function
- The total revenue curve of a firm is R (q) = 40q - 12q2 and its average cost A(q) = 1/30q2 - 12.85q +20 + 400/q, where q is the firm's output. (1) Derive and expression C(q) for the firm's total cost function.Suppose a company's revenue function is given by R(q)=−q3+400q2R(q)=-q3+400q2 and its cost function is given by C(q)=550+12qC(q)=550+12q, where qq is hundreds of units sold/produced, while R(q)R(q) and C(q)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)=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.)Assume a firm has the following total cost function and revenue functions; TC = ½ Q2 -6Q2 + 6Q + 7 and TR = 30Q – Q2 where Q is measured in tonnes and costs and revenues are measured in dollars. a. Find the level of output that maximize total revenue b. Find the level of output that maximizes profits. Calculate MR and MC at this value of Q. What do you observe?
- Answer B,C,D A firm can produce at most x = 2500 units per month, and their marginal cost function has been computed to be MC=1200+x , while the cost of producing and selling 30 units is $70,000. If their marginal revenue function has been computed to be MR=3500 , then find: The number of units of production resulting in maximum monthly profit The maximum monthly profit Associated fixed costs How many units does the firm need to manufacture and sell in order to break even?A firm's demand and total cost function are given by the expression: P = 20 - Q/2 (1) TC = 0.5Q2 + 36 (2) Where P is price per unit in £ TC = total cost in £ Q is quantity demanded and produced. Find the profit-maximising level of output using the profit function and calculate how much profit is made at this output level.Suppose a product's revenue function is given by R(q)=−6q2+400q, where R(q)is in dollars and qis units sold. Also, it's cost function is given by C(q)=103q+3333, where C(q)is in dollars and qis units produced. Find a simplified expression for the item's Marginal Profit function ( MP(q)) and record your answer in the box. Be sure to use the correct variable. (Use the Preview button to check your syntax before submitting your final result). Answer: MP(q)=
- The demand function for a firm is; Qd = 122,000 - 500P + 4M +10,000PR where, Qd is quantity demanded, P is price per unit. M is income, and PR the price of a related good. The estimated the valueS of M and PR will be Rs 3200 and Rs 4, respectively. The firm's estimated average variable coSt function IS; AVC = 500 - 0.03Q + 0.000001Q2 a. Find the profit maximizing level of output of the firm and the price to charge. b. Should the manager continue production or shut down? Explain your answer. c. Find the level of output at which the average variable cost is at its minimum.(i) If the demand function for a particular commodity is p=−0.09x+51 and the total cost function C(x)=1.32x2+11.7x+101.4,where x is the level of production. Find (a) The revenue R(x) and profit Π(x). (b) All values of x for which production of the commodity is profitable. (ii) The total cost of manufacturing x units during the daily production run at a factory,is C(x)= x2+ x+900 dollars. Usually,x(t)=25t units are manufactured during the first t hours of production. (a) Express the total manufacturing cost as a function of t. (b) How much will have been spent on production by the end of the third hour? (c) When will the total manufacturing cost reach $11,000?he total revenue curve of a firm is R(q)=40q−12q and its average cost A(q)=130q−12.85q+20 +400q,where q is the firms output. i. Derive an expression C(q) for the firms total cost function. ii. Derive an expression Π(q) for the firms profit function. iii. Is the rate of change of profit increasing or decreasing when the ouput level of the firm is 10 units? iv. Determine the level of output for which the firms profit is maximized. v. What is the firmss maximum profit?