Given Cost and Price (demand) functions C(q)=120q+45000 and p(q)=−2.8q+900, what is the marginal revenue when costs are $80,000? The marginal revenue is ____dollars per item.
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- Your college newspaper, The Collegiate Investigator, sells for 90¢ per copy. The cost of producing x copies of an edition is given by C(x) = 70 + 0.10x + 0.001x2 dollars. (a) Calculate the marginal revenue R'(x) and profit P'(x) functions. HINT [See Example 2.] R'(x) = P'(x) = (b) Compute the revenue and profit, and also the marginal revenue and profit, if you have produced and sold 500 copies of the latest edition. revenue $ profit $ marginal revenue $ per additional copy marginal profit $ per additional copy Interpret the results. The approximate from the sale of the 501st copy is $ . (c) For which value of x is the marginal profit zero?x = copiesInterpret your answer. The graph of the profit function is a parabola with a vertex at x = , so the profit is at a maximum when you produce and sell copies.A company is the sole producer of holographic TVs. The daily demand for these TVs is Q=10,200 - 100P, where Q is the quantity demanded and P is the price. The cost of producing the TVs is (note that this implies that marginal cost is equal to Q, MC = Q). What is the company’s total revenue schedule? What is the company’s marginal revenue schedule? What is the profit maximising number of TVs that the company must produce each day? What price should it charge per TV? What is the daily profit?You sell items. Your marginal revenue and marginal cost are given by the formulas: MR (q)= 9.344-0.8q and MC (q)= 0.1q2-1.2q+5.9 where q is measured in hundreds of items and marginal revenue and marginal cost are in dollars per item. Compute the change in total cost that occurs if quantity increases from 225 to 226 items.
- Q1. 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 = 50Q + 30,000. Assuming the firm maximizes profits, a. What is the level of production?The demand function for a particular product is given by D(x)=0.5x^2+3x+190‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾√D(x)=0.5x^2+3x+190 dollars, where x is the number of units sold. What is the marginal revenue when 88 items are sold? Round your answer to 2 decimal places. D(x)=0.5x^2+3x+190‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾Assume that a firm’s marginal revenue curve intersects the rising portion of its marginal cost curve at 500 units of output. At this output level, a profit-maximizing firm’s total cost of production is $1,000. If the price of the product is $5 per unit, the total revenue earned by the firm will be:
- The demand and total profit function, P(x) for rooms in a hotel are given as follows. 3x = 600 - P P(x) = 450x – 3.5x2 - 4000 Where p is the price in ringgit per room and x is the quantity of room rented. Determine the marginal cost when 2 rooms are rentedA 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. Use equation (1) to find the total revenue (TR) function and determine the total revenue maximising output. Calculate the profit associated with this level of output.Consider the total revenue function, TR = 53 + 8Q + 6Q^2 Find the marginal revenue (MR) at Q= 6.
- Suppose the revenue function y=R(x) is linear, and points (x,y) of (10,550) and (13,715) are on the line. a. What is the marginal revenue? b. Suppose also the total costs are given by C(X) = 150 + 15x +2x^2. Find the x-value that maximizes profit.If marginal cost MC = 2.5 (assume this is constant), calculate the profit-maximising price and the revenue maximising price. In doing so, remember thatA firm has the following revenue and cost functions. TR = 60 Q – Q^2TC = 1/2 Q^2 +30Q + 30Determine the quantity level at which the firm maximizes its total profit.(Hint: use marginal revenue = marginal cost rule)