QUESTION 1

For the cost and price functions below, find (a) the number, q, of units that produces maximum prot; (b) the price, p, in dollars per unit that produces maximum profit; and (c) the maximum prot, P, in dollars. C(q) = 30 + zoqe- 0-02q; p = 803' 0.02q Find the profit function, P. PM) = (a) The number, q, of units that produces maximum prot is q = (Do not round until the final answer. Then round to the nearest whole number as needed.) (b) The price, p, per unit that produces maximum prot is p = $D. (Do not round until the final answer. Then round to the nearest cent as needed.) (c) The maximum prot is P = 35 (Do not round until the final answer. Then round to the nearest cent as needed.) A local club is arranging a charter flight to Hawaii. The cost of the trip is $531 each for 83 passengers, with a refund of $5 per passenger for each passenger in excess of 83. a. Find the number of passengers that will maximize the revenue received from the flight. b. Find the maximum revenue. .. . a. The number of passengers that will maximize the revenue received from the flight is (Round to the nearest integer as needed.) b. The maximum revenue is $Suppose that the graph shown is the graph of f'(x), the derivative off(x). Find the open intervals where the original function is concave upward or concave downward. Find any inection points. Find any inection points. Select the correct choice below and, if necessary, ll in the answer box to complete your choice. O A- The original function has (an) inection point(s) at x = (Round to the nearest integer as needed. Use a comma to separate answers as needed.) O B. The original function has no inection points. Find the open intervals where the function f is concave upward. Select the correct choice below and, if necessary. ll in the answer box to complete your choice. O A- The original function is concave upward on the interval(s) (Type your answer in interval notation. Use a comma to separate answers as needed.) O B. The original function is never concave upward. Find the open intervals where the function f is concave downward. Select the correct choice below and. if necessary. ll in the answer box to complete your choice. O A- The original function is concave downward on the interval(s) (Type your answer in interval notation. Use a comma to separate answers as needed.) O B. The original function is never concave downward. Find the absolute extrema if they exist, as well as all values of x where they occur, for the function 1 5 f(x) = gxa - 5x2 + 4x 1 on the domain [0,5]. Select the correct choice below and, if necessary, ll in the answer boxes to complete your choice. U A- The absolute maximum is , which occurs at x = (Round the absolute maximum to two decimal places as needed. Type an exact answer for the value of x where the maximum occurs. Use a comma to separate answers as needed.) .; 2- B. There is no absolute maximum. Select the correct choice below and, if necessary, ll in the answer boxes to complete your choice. '3' A- The absolute minimum is , which occurs atx = (Round the absolute minimum to two decimal places as needed. Type an exact answer for the value of x where the minimum occurs. Use a comma to separate answers as needed.) .; 2- B. There is no absolute minimum. 'X x2+6- Find the absolute extrema if they exist, as well as all values of x where they occur, for the function f(x) = Select the correct choice below and, if necessary, ll in the answer boxes to complete your choice. U A- The absolute maximum is , which occurs at x = (Round the absolute maximum to two decimal places as needed. Type an exact answer for the value of x where the maximum occurs. Use a comma to separate answers as needed.) .; 2- B. There is no absolute maximum. Select the correct choice below and, if necessary, ll in the answer boxes to complete your choice. U A- The absolute minimum is , which occurs atx = (Round the absolute minimum to two decimal places as needed. Type an exact answer for the value of x where the minimum occurs. Use a comma to separate answers as needed.) .; 2- B. There is no absolute minimum