Pierce Manufacturing determines that the daily revenue, in dollars, from the sale otx lawn chairs is R(x) =0.006x3 + 0.042(2 + 0.7x. Currently, Pierce sells 80 lawn chairs daily. a) What is the current daily revenue? b) How much would revenue increase if 82 lawn chairs were sold each day? c) What is the marginal revenue when 80 lawn chairs are sold daily? cl) Use the answer from part (c) to estimate R(81), R(82), and R(83). a) The current revenue is $ b) The revenue would increase by $ . (Round to the nearest cent.) c) The marginal revenue is 35 when 80 lawn chairs are sold daily. d) R(81) m $7 (Round to the nearest cent as needed. Use the answer from part c to answer this part.) R(82) m 35 (Round to the nearest cent as needed. Use the answer from part c to answer this part.) R(83) m 33 (Round to the nearest cent as needed. Use the answer from part c to answer this part.) Find the absolute extrema of the function, if they exist, over the indicated interval. Also indicate the x-value at which each extremum occurs. If no interval is specified, use the real numbers, ( - co,co). f(x) = Vx; [0,1] Alifeguard needs to rope off a rectangular swimming area in front of Long Lake Beach, using 2500 yd of rope and floats. What dimensions of the rectangle will maximize the area? What is the maximum area? (Note that the shoreline is one side of the rectangle.) Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. O A. The absolute maximum is at x= and the absolute minimum is |atx = Let x be the length of a side of the rectangle perpendicular to the shoreline. Write the objective function for the area in terms of x. Use a comma to separate answers as needed.) A(x) = O B. The absolute minimum is at x = and there is no absolute maximum. (Type an expression using x as the variable.) (Use a comma to separate answers as needed.) O C. The absolute maximum is at x = and there is no absolute minimum. The length of the shorter side of the rectangular region is (Use a comma to separate answers as needed.) The length of the longer side of the rectangular region is O D. There is no absolute maximum and no absolute minimum. The maximum area of the rectangular region is Find the absolute maximum and minimum values of the function, if they exist, over the indicated interval. Also indicate the x-value at which each extremum occurs. Pierce Manufacturing determines that the daily revenue, in dollars, from the sale of x lawn chairs is R(x) = 0.006x + 0.04x" +0.7x. Currently, Pierce sells 80 lawn chairs daily. f(x) = 4x ; [-27,27] a) What is the current daily revenue? b) How much would revenue increase if 82 lawn chairs were sold each day? c) What is the marginal revenue when 80 lawn chairs are sold daily? d) Use the answer from part (c) to estimate R(81), R(82), and R(83). Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. O A. The absolute maximum value is |at x = and the absolute minimum value is |atx=. a) The current revenue is $. (Use a comma to separate answers as needed. b) The revenue would increase by $ ]. (Round to the nearest cent.) O B. The absolute maximum value is |at x = and there is no absolute minimum. (Use a comma to separate answers as needed.) c) The marginal revenue is $ | when 80 lawn chairs are sold daily. O C. The absolute minimum value is |at x= and there is no absolute maximum. d) R(81) ~ $ (Use a comma to separate answers as needed.) Round to the nearest cent as needed. Use the answer from part c to answer this part.) O D. There is no absolute minimum and there is no absolute maximum. R(82) ~ $ Round to the nearest cent as needed. Use the answer from part c to answer this part.) R(83) ~ $ (Round to the nearest cent as needed. Use the answer from part c to answer this part.)