Given cost and price (demand) functions C(q) = 110q + 40,800 and p(q) = - 1.9q + 900, what is the marginal revenue at a production level of 55 items? The marginal revenue is dollars per item. (Round answer to nearest dollar.) Given cost and price (demand) functions C(q) = 110q + 44,700 and p(q) = - 2q + 900, what profit can the compnay earn by selling 50 items? in profit. It can expect to earn $ (Round answer to nearest dollar.) Given Cost and Price (demand) functions C(q) = 100q + 40000 and p(q) = - 2.4q + 800, what is the marginal revenue when costs are $70,000? The marginal revenue is dollars per item. Given Cost and Price (demand) functions C(q) = 110q + 45000 and p(q) = -2.8q + 800, what profit can be earned if the price is set to be $550 per item? The profit is $ (Round to the nearest cent.)
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- Given cost and price (demand) functions C(g)= 110q + 44,600 and p(g) = - 2g + 860, what is the marginal revenue at a production level of 55 items? The marginal revenue is $ . (Round answer to nearest dollar.) Pr rithAverage and marginal profit Let C(x) represent the cost ofproducing x items and p(x) be the sale price per item if x items aresold. The profit P(x) of selling x items is P(x) = xp(x) - C(x)(revenue minus costs). The average profit per item when x items aresold is P(x)/x and the marginal profit is dP/dx. The marginal profitapproximates the profit obtained by selling one more item, given that x items have already been sold. Consider the following cost functions Cand price functions p.a. Find the profit function P.b. Find the average profit function and the marginal profit function.c. Find the average profit and the marginal profit if x = a units are sold.d. Interpret the meaning of the values obtained in part (c). C(x) = -0.02x2 + 50x + 100, p(x) = 100 - 0.1x, a = 500X If total revenue received from the sale of x items is given by R(x) = 10 In (4x + 1), while the total cost to produce x items is C(x) = ¹ (a) The marginal revenue (b) The profit function P(x) (c) The marginal profit when x = 40 (d) Interpret the results of part (c). (a) How can the marginal revenue be found? A. Find R(x) - C(x). B. Find the derivative of R(x). C. Find the derivative of R(x) - C(x). R( 2 ). D. Find R find the following.
- Given Cost and Price (demand) functions C(q) = 110q + 45000 and p(q) = - 2.8q + 800, what profit can be earned if the price is set to be $550 per item? U The profit is $ 1,?9 (Round to the nearest cent.) A company produces a special new type of TV. The company has fixed costs of $499,000, and it costs STT00 to produce each TV. The company projects that if it charges a price of $2300 for the TV, it will be able to sell 850 TVs. If the company wants to sell 900 TVs, however, it must lower the price to $2000. Assumo a linear demand. What is the marginal profit if 200 TVs are produced It is $ 0 per item. (Round answer to nearest dollar.)The table shows the marginal cost C'), the marginal revenue R'(x) for producing x items. The third column, P'(x). is partially completed. All values are in dollars per item. (a) Complete the remaining entries in the third column. (b) What does the table tell you about the revenue function? (c) Find the production level that maximizes profit. (a) Complete the remaining entries in the third column of the table on the right. c'(x) R'(x) P'(x) -21 62 41 (b) What does the table tell you about the revenue function? Select one and complete the box, if necessary. 10 41 41 40 14 41 O A. Items sell for $ each. 70 41 41 O B. There is not enough information to determine anything about the revenue function. 90 206 41 - 165 (c) Find the production level that maximizes profit. Profit P(x) is a maximum when x= items are produced.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) = 60 + 0.10x + 0.001x² dollars. (a) Calculate the marginal profit function, in dollars per copy. P'(x) = (b) Compute the marginal profit, if you have produced and sold 500 copies of the latest edition. When you produce and sell 500 copies, the marginal profit is dollars per copy. Interpret the results: The approximate loss from the production and sale of the 501st сорy is dollars.
- Suppose that a demand equation is given by q=1750-25p and the cost of producing q units is given by C(q) = 63,000-70q+0.02q2. Find the marginal profit for the following production levels. (a) 700 units (b) 1055 units (c) 1600 units (a) The marginal profit for a production level of 700 units is (Simplify your answer.)11.2 The cost, in thousands of dollars, of airing x television commercials during a sports event is given by C(x) = 20 + 3,000x + 0.01x2. (a) Find the marginal cost function C'(x). HINT [See Example 1.] C'(x) = Use it to estimate how fast the cost is increasing when x = 4. thousand dollars per television commercialCompare this with the exact cost of airing the fifth commercial. The cost is going up at the rate of $ per television commercial. The exact cost of airing the fifth commercial is $ . Thus, there is a difference of $ . (b) Find the average cost function C, and evaluate C(4). HINT [See Example 2.] C(x) = C(4) = thousand dollars per television commercial What does the answer tell you? The average cost of airing the first four commercials is $ per commercial.A startup software company has indicated its cost, c(x), and revenue, f(x), as given below, such that x is the number of lines of programing code (units in 1000 lines). c(x) = 80000 - 2(x-200)2 f(x) = (x-10)3 + (x+10)2 Find the marginal cost analytically, and draw its graph Find the marginal revenue analytically, and draw its graph Solve for the x point where marginal cost is equal to marginal revenue analytically. Comment why is this point significant analytically. Write the profit function and draw its graph Is the profit function concave up or concave down?
- The cost of producing x teddy bears per day at the Cuddly Companion Co. is calculated by their marketing staff to be given by the formula C(x) = 100 + 37x - 0.07x2. (a) Find the marginal cost function C'(x). C'(x) = (b) How fast is the cost going up at a production level of 100 teddy bears? When they produce 100 teddy bears, the production costs are increasing at a rate of x dollars per teddy bear In other words, the cost to produce the 101st teddy bear is approximately dollars (c) Find the average cost function C, and evaluate C(100). C(x) = C(100) = So when they produce 100 teddy bears, the average cost per teddy bear is x dollars. (d) Fill in the blanks: Since the marginal cost is less than the average cost per unit, increasing production from 100 teddy bears will cause the average cost per unit to decrease.The cost of producing x teddy bears per day at the Cuddly Companion Co. is calculated by their marketing staff to be given by the formula Cx) - 100 + 40x - 0.08. (a) Find the marginal cost function C(x). Cx) = 40 - 0.16x Use it to determine how fast the cost is going up (in s) at a production level of 100 teddy bears $ 24 per teddy bear Compare this with the exact cost of produong the 101" teddy bear (in ). The cost is increasing at a rate of s 24 per teddy bear. The exact cost of producing the 101" teddy bear is s Thus, there is a diference of (b) Find the average cost function C, and evaluate č100) (in s). C100) -s x per teddy bear What does the answer tell you? per teddy bear. The average cost of producing the first hundred teddy bears is s Eter an tuber2) 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?