C the marginal cost of a cup of coee is the cost of

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Unformatted text preview: ost of producing the first cup. (C) The marginal cost of a cup of coffee is the cost of producing one additional cup. (D) The marginal cost of a cup of coffee is the cost of producing zero cups. (E) None of these. 14. A product has a production cost function C (x) = 460x + 6670 and a revenue function R(x) = 575x. Find and analyze the break-even quantity, then find the profit function. Answer parts (i) and (ii) below. (i) The break-even quantity is (A) less than 30 units (B) between 30 units and 40 units (C) between 40 units and 50 units (D) between 50 units and 60 units (E) more than 60 units (ii) Choose the correct profit function. (A) P (x) = 6670 − 115x (B) P (x) = 1035x + 6670 (D) P (x) = 115x − 6670 (E) None of these (C) P (x) = 575x 15. Joanne sells silk-screened T-shirts at community festivals and craft fairs. Her marginal cost to produce one T-shirt is $3.50. Her total cost to produce 40 T-shirts is $230, and she sells them for $7 each. How many T-shirts must she produce and sell in order to break even? (A) less than 15 (B) between 15 and 30 (D) between 45 and 60 (E) more than 60 (C) between 30 and 45 16. The graph below shows supply and demand for a product Answer parts (i) through (iii) below. (i) At the equilibrium point for this product, p = q= (ii) The price p = 30 is the equilibrium price. At this price, how many items are suppliers willing to produce? How many items do consumers want to buy? Use your answers to these questions to explain why, if prices are the equilibrium price, the market tends to push prices (toward the equilibrium). (iii) The price p = 10 is the equilibrium price. At this price, how many items are suppliers willing to produce? How many items do consumers want to buy? Use your answers to these questions to explain why, if prices are the equilibrium price, the market tends to push prices (toward the equilibrium). 2 17. Let one week’s supply and demand functions for gasoline be given by p = D(q ) = 300 − q and 5 4 p = S (q ) = q , where p is the price in dollars and q is the number of 42-gallon barrels. Answer parts 5 (i) and (ii) below. (i) Graph these equations on the same axes. (ii) Find the equilibrium price. 18. Find the domain of the function f (x) = x2 3 . −4 (A) (−∞, −2) ∪ (−2, 2) ∪ (2, ∞) (B) (−∞, ∞) (D) (−∞, 0) ∪ (0, ∞) (C) (2, ∞) (E) None of these 19. Indicate whether the graph specifies a function. (A) The graph does specify a function (B) The graph does not specify a function 20. Let Answer parts (i) through (iii) 2x + 2 x−9 f ( x) = 2 if x ￿= 9 if x = 9 (i) Find the value of f (9). (A) less than -1 (B) between -1 and 1 (D) between 3 and 5 (C) between 1 and 3 (E) more than 5 1 (ii) Find the value of f (− 2 ). (A) less than -1 (B) between -1 and 1 (D) between 3 and 5 (C) between 1 and 3 (E) more than 5 (iii) Find the value of x such that f (x) = 1. (A) less than -5 (B) between -5 and 5 (D) between 15 and 25 (E) more than 25 (C) between 5 and 15 21. Income ta...
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