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- A commodity has a demand function modeled by p = 106 − 0.5x and a total cost function modeled by C = 30x + 33.75, where x is the number of units. (a) What unit price (in dollars) yields a maximum profit? $ per unit (b) When the profit is maximized, what is the average cost (in dollars) per unit? (Round your answer to two decimal places.) $ per unitLet's say jacky has a demand function for a product made in Ney york city given that the function D(q)=-1.15q+270, where q is the number of items in demand and D(q) is the price per item, in dollars, that can be charged when q units are sold. Say that the fixed costs of production for the item is $5,000 and variable costs are $10 per item produced. If 100 items are produced and sold, what are the finds :A commodity has a demand function modeled by p = 117 − 0.5x and a total cost function modeled by C = 40x + 31.75, where x is the number of units. (a) What price yields a maximum profit? $____________ per unit (b) When the profit is maximized, what is the average cost per unit? (Round your answer to two decimal places.) $_____________ per unit
- Define Q to be the level of output produced and sold, and assume that the firm’s cost function is given by the relationshipTC = 20 + 5Q + Q2Furthermore, assume that the demand for the output of the firm is a function of price P given by the relationshipQ = 25 - Pa. Define total profit as the difference between total revenue and total cost, and express in terms of Q the total profit function for the firm. (Note: Total revenue equals price per unit times the number of units sold.)b. Determine the output level where total profits are maximized.When Apple introduced its first portable media player, the iPod, its constant marginal cost of producing the top-of-the-line model was $200 (iSuppli), its fixed cost was approximately $736 million, and we estimate that its inverse demand function was p = 600 - 25Q, where Q is units measured in millions. Be sure to express your answers in the proper units, where needed. a. What was Apple's average cost function? b. Assuming that Apple was maximizing its short-run monopoly profit, what was its marginal revenue function? c. What were its profit-maximizing price, quantity, profit and Lerner Index? d. What was the price elasticity of demandSergio Lopez is a publisher of Latin American poetry. His fixed cost is $525, and the cost to produce each individual copy of his book is $3.50. Currently, Sergio is selling these books for $6 each. So far this year, he has produced x a. Write a linear cost function C for Sergio’s book production, in terms of x. b. Find the linear revenue function R for selling x copies of the book. Remember that P(x) = (price)x. c. Use and 1b. to determine the profit function P for selling x books. Write the formula in simplified form. d.Use your answer for 1c to determine the profit, in dollars, for selling 300 books.
- 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)=Suppose a company has fixed costs of $31,200 and variable cost per unit of 1 3 x + 444 dollars, where x is the total number of units produced. Suppose further that the selling price of its product is 1768 − 2 3 x dollars per unit. Find the break-even points. (Enter your answers as a comma-separated list.) Find the maximum revenue. (Round your answer to the nearest cent.) Form the profit function P(x) from the cost and revenue functions. Find maximum profit. What price will maximize the profit? (Round your answer to the nearest cent.)Suppose a company has fixed costs of $1500 and variable costs of (3/4)x + 1120 dollars per unit, where x is the total number of units produced. Suppose further that the selling price of its product is 1200 − (1/4)x dollars per unit. (a) Find the break-even points. (Enter your answers as a comma-separated list.)x = (b) Find the maximum revenue. (Round your answer to the nearest cent)$ (c) Form the profit function, P(x), from the cost and revenue functions.P(x) = Find maximum profit. (Round your answer to the nearest cent.)$ (d) What price will maximize the profit? (Round your answer to the nearest cent.)
- . An electricity producer has a constant marginal cost of production equal to $40 per megawatt. The residual demand for its electricity is given by P (q) = a−bq, where P is the price and q is the quantity of power generated by this producer. The producer knows the slope, b, but he vertical intercept of the residual demand curve, a is unknown. Assume A and B are greater than zero. If you get stuck, you may answer any of the following questions for special case where a = 80 And b = 0.5 for partial credit. (a) What is the marginal revenue, M R(q), for this producer? b) What is the optimal q for this producer? (c) What is the electricity producer’s optimal price? (d) What is the electricity producer’s optimal bid in a uniform price Auction? e) Suppose b is equal to zero. Would the producer have an incentive to submit a bid above its marginal cost? Explain.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 donut shp has a fixed cost of $92000 per day and a varibale cost of $2 for each donut produced. If the donuts are sold to distributors for $5 each. What is the price-demand function? What is the revenue function?