Consider the following cost function. a. Find the average cost and marginal cost functions. b. Determine the average and marginal cost when x = a. c. Interpret the values obtained in part (b). C(xx) = 1800 + 0.6x, 0 sxs 5000, a = 2400 a. The average cost function is C(o) = - The marginal cost function is C'(x) = - b. The average cost when x = 2400 is $ - (Round to two decimal places as needed.) The marginal cost when x = 2400 is $ per item. (Round to two decimal places as needed.) C. The average cost per item is about $| when items are produced. (Round to two decimal places as needed.) The cost of producing the 2401st item is $ (Round to two decimal places as needed.)Let C(x) represent the cost of producing x items and p(x) be the sale price per item if x items are sold. 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 are sold is- P(x) - and the marginal profit is - The marginal profit approximates the profit obtained by selling one more item given that x items have already been sold. Consider the following cost functions C and price functions p. Complete parts a through d below. C(x)= - 0.03x" + 60x + 300, p(x) =200 -0.1x, a = 800 a. Find the profit function P. The profit function is P(x) = 1- b. Find the average profit function and marginal profit function. The average profit function is - The marginal profit function is -= 1. c. Find the average profit and marginal profit if x = a units have been sold. The average profit if x = a units have been sold is $ 1 (Round to two decimal places as needed.) The marginal profit if x = a units have been sold is $ 1 (Round to two decimal places as needed.) d. Interpret the meaning of the values obtained in part c. Interpret the average profit if x = a units have been sold. Select the correct choice below and fill in any answer box(es) within your choice Type integers or decimals rounded to the nearest hundredth as needed.) O A. The average profit per item for each of the first |items produced is $. O B. The profit for the items produced is S O C. The average profit for the first |items produced is $ O D. The profit for the 801st item produced is so Interpret the marginal profit if x = a units have been sold. Select the correct choice below and fill in any answer box(es) within your choice. (Type integers or decimals rounded to the nearest hundredth as needed.) O A. The profit per item for each of the first items produced is S. O B. The profit for the 801st item produced is $ 2]. O C. The marginal profit for the first items produced is S. O D. The profit for the items produced is SLet C(x) represent the cost of producing x items and p(x) be the sale price per item if x items are sold. 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 are sold is P(x)/x and the marginal profit is dP/dx. The marginal profit approximates the profit obtained by selling one item given that x items have already been sold. Consider the following cost function C and price function p a. Find the profit function P b. Find the average profit function and marginal profit function. c. Find the average profit and marginal profit if x = a units have been sold. d. Interpret the meaning of the values obtained in part (c). C(x)= - 0.04x~ + 100x + 800, p(x) =200, a = 1000 a. The profit function is P(x) = 0.04x~ + 100x - 800 b. The average profit function is - ! = 22. The marginal profit function is - = 0.08x + 100 c. The average profit if x = a units have been sold is 0.08a + 100 (Simplify your answer. Round to one decimal place as needed.) The marginal profit if x = a units have been sold is 179.92. (Simplify your answer. Round to one decimal place as needed.) d. Interpret the average profit if x = a units have been sold. Choose the correct answer below. O A. The average profit for the first 1000 items produced is $139.20. O B. The profit for the 1001st item produced is approximately $180.00. O C. The profit for the 180 items produced is approximately $1000.00. O D. The average profit per item for each of the first 1000 items produced is $139.20. Interpret the marginal profit if x = a units have been sold. Choose the correct answer below. O A. The profit for the 180 items produced is approximately $1000.00. O B. The marginal profit for the first 1000 items produced is approximately $139.20. O C. The profit for the 1001st item produced is approximately $180.00. O D. The profit per item for each of the first 1000 items produced is approximately $139.20.Consider the following cost function. a. Find the average cost and marginal cost functions. b. Determine the average and marginal cost when x = a. C. Interpret the values obtained in part (b). C(x) =0.01x# + 0.3x~ + 20x + 140, 0 sx = 1500, a = 500 a. The average cost function is C(xx) = 440.7 The marginal cost is function is C'(x() = [1. b. The average cost when * = a is $ 1. (Round to two decimal places as needed.) The marginal cost when x = a is $ 1. (Round to two decimal places as needed.) c. Choose the correct interpretation of the average cost when x = a. O A. The cost of producing the 501st item is about $1,724.32. O B. The average cost per item is about $2,670.28 when 500 items are produced. O C. The cost of producing 500 items is about $1,470.26 O D. The cost of producing the 501st item is about $7,820.00. Choose the correct interpretation of the marginal cost when x = a. O A. The cost of producing 501 items is about $324.32. O B. The cost of producing 500 items is about $1,470.28. O C. The cost of producing the 501st item is about $7,820.00. O D. The average cost per item is about $2,670.28 when 500 items are produced.Let C(x) represent the cost of producing x items and p(x) be the sale price per item if x items are sold. 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 are sold is P(x)/x and the marginal profit is dP/dx. The marginal profit approximates the profit obtained by selling one more item given that x items have already been sold. Consider the following cost functions C and price functions p. Complete parts (a) through (d) below. C(x) = - 0.05x- + 50x + 100, p(x) = 200, a = 500 a. Find the profit function P. The profit function is P(x) = 0.05x~ + 150x - 100. b. Find the average profit function and marginal profit function. The average profit function is - P(xx) x = 0.10x + 150 dP The marginal profit function is - dx = 0.10a + 150 C. Find the average profit and marginal profit if x = a units have been sold. The average profit if x = a units have been sold is $ 174.8 . (Type an integer or a decimal.) The marginal profit if x = a units have been sold is $ 29910 (Type an integer or a decimal.) d. Interpret the meaning of the values obtained in part (c). Interpret the average profit if x = a units have been sold. Choose the correct answer below. O A. The profit for the 200 items produced is $500.00 O B. The average profit per item for each of the first 500 items produced is $174.80. O C. The profit for the 501st item produced is $200.00 O D. The average profit for the first 500 items produced is $174.80. Interpret the marginal profit if x = a units have been sold. Choose the correct answer below. O A. The marginal profit for the first 500 items produced is $174.80. O B. The profit per item for each of the first 500 items produced is $174.80. O C. The profit for the 501st item produced is $200.00 O D. The profit for the 200 items produced is $500.00