Total revenue is in dollars and x is the number of units. Suppose that the total revenue function for a commodity is R = 64x 0.02x2. (a) Find R(100). $|:l Tell what it represents. 0 The revenue increases by about this amount when the number of units is increased from 100 to 101. O 100 units produce this amount of revenue. 0 The revenue decreases by about this amount when the number of units is increased from 100 to 101. O 101 units produce this amount of revenue. 0 The actual revenue of the 100th unit is this amount. (b) Find the marginal revenue function. (c) Find the marginal revenue (in dollars per unit) at x = 100. $ l:] per unit Tell what it predicts about the sale of the next unit and the next 3 units. The sale of the next unit will the revenue by about $ :' . The sale of the next 3 units will the revenue by about $ :| . (d) Find R(101) - R(100). $|:l Explain what this value represents. 0 marginal revenue at x = 100 0 actual revenue from the 100th unit 0 actual revenue from 101 units 0 actual revenue from the 1015t unit 0 actual revenue from 100 units Total revenue is in dollars and x is the number of units. Suppose that the total revenue function for a commodity is R(X) = 46x 0.05x2. (a) Find R(50). $|:l Tell what it represents. 0 The revenue decreases by about this amount when the number of units is increased from 50 to 51. O The revenue increases by about this amount when the number of units is increased from 50 to 51. O 50 units produce this amount of revenue. O The actual revenue of the 50th unit is this amount. 0 51 units produce this amount of revenue. (b) Find the marginal revenue function. (c) Find the marginal revenue (in dollars per unit) at x = 50. $ l: per unit Tell what it predicts about the sale of the next unit and the next 2 units. The sale of the next unit will the revenue by about $ :] . The sale of the next 2 units will the revenue by about $ :l . (d) Find R(51) R(50). $ |:l Explain what this value represents. 0 actual revenue from 51 units 0 actual revenue from the Slst unit 0 marginal revenue at x = 50 O actual revenue from 50 units 0 actual revenue from the 50th unit Suppose that demand for local cable TV service is given by p = 122 0.4x where p is the monthly price per subscriber in dollars and x is the number of subscribers (in hundreds). (a) Find the total revenue R (in hundreds of dollars) as a function of the number of subscribers (in hundreds). (b) Find the number of subscribers (in hundreds) when the company charges $80 per month for cable service. :] hundred subscribers Find the total revenue (in hundreds of dollars) forp = $80. :] hundred dollars (c) How could the company attract more subscribers? More subscribers are attracted by prices. (d) Find the marginal revenue (in hundreds of dollars per hundred subscribers) when the price is $80 per month. :] hundred dollars per hundred subscribers Interpret this value. For the number of subscribers associated with a price of $80 per month, as the number of subscribers (in hundreds) increases by l, the revenue by |:] (100) = $ |:|. What does the marginal revenue suggest about the monthly charge to subscribers? O The revenue can be increased by lowering the monthly charges. 0 The revenue can be increased by raising the monthly charges. Total revenue is in dollars and x is the number of units. Suppose that in a monopoly market, the demand function for a product is given by p = 390 0.2x where x is the number of units and p is the price in dollars. (a) Find the total revenue from the sale of 500 units. $|:| (b) Find the marginal revenue W at 500 units. m = 2am Interpret this value. 0 The 5015t unit will lose |MR| dollars more in revenue. 0 The 5015t unit will bring in ll dollars more in revenue. O The 5015t unit will lose lml hundred dollars more in revenue. 0 The 5015t unit will bring in ll hundred dollars more in revenue. (c) Is more revenue expected from the 5015t unit sold or from the 701st? Explain. The 7015t unit will bring in :15 :l more in revenue. Thus the unit will bring in more revenue. Cost is in dollars and X is the number of units. Find the marginal cost functions mfor the given cost function. C = 400 + 34x + 5x3 Suppose that the cost function for a commodity is C(x) = 30 + x2 dollars. (a) Find the marginal cost atx = 3 units. M730) = E Tell what this predicts about the cost of producing 1 additional unit. The cost to produce the 4th unit is predicted to be $ :| . (b) Calculate C(4) (2(3) to find the actual cost of producing 1 additional unit. $|:l The graph of a company's total cost function is shown. Use the graph to answer the following questions. C(x) 40,000 E 30.000 E 20.000 10,000 _r 200 400 600 Units (D (a) Will the 151st item or the 4515t item cost more to produce? Explain. The 151st unit will cost than the 451st unit, since c'(150) is than c'(450), and the slope gives the cost of the next unit. (b) Does this total cost function represent a manufacturing process that is getting more efficient or less efficient? Explain. The manufacturing process is becoming efficient. Since the slope is , the cost of each additional unit is than the previous unit. Nppd len? \"W\" Cost, revenue, and profit are in dollars and X is the number of units. Suppose that the total revenue function for a product is R(X) = 35x and that the total cost function is C(x) = 1500 + 15x + 0.01x2. (a) Find the profit from the production and sale of 500 units. $|:l (b) Find the marginal profit function. E (c) Find M7 at x = 500. we: Explain what it predicts. The total profit will by approximately $ :' on the sale of the next (SOlst) unit. (d) Find P(501) P(500). $|:l Explain what this value represents. 0 This is the actual revenue on the sale of the 5015t unit. 0 This is the actual cost of the 5015t unit. 0 This is the total cost of 501 units. 0 This is the actual profit on the sale of the 5015t unit. 0 This is the total profit for 501 units. Cost, revenue, and profit are in dollars and x is the number of units. Suppose that the total revenue function is given by R(X) = 47x and that the total cost function is given by C(x) = 100 + 30x + 0.1x2. (a) Find P(100). P(100) = (b) Find the marginal profit function MP. MP = (c) Find MP at x = 100. MP(100) = Explain what it predicts. O At x = 100, MP(100) predicts that cost will increase by |MP(100) | dollars. At x = 100, MP(100) predicts that cost will decrease by | MP(100) | dollars. At x = 100, MP(100) predicts that profit will decrease by |MP(100) | dollars. O At x = 100, MP(100) predicts that profit will increase by | MP(100) | dollars. (d) Find P(101) - P(100). tA Explain what this value represents. O The sale of the 100th unit will decrease profit by [P(101) - P(100) | dollars. The sale of the 100th unit will increase profit by [P(101) - P(100) | dollars. The sale of the 101st unit will increase profit by [P(101) - P(100) | dollars. O The sale of the 101st unit will decrease profit by [P(101) - P(100) | dollars