The Boogie-All-Night Company manufactures black lights for night clubs. Suppose the company's business software reveals that the monthly xed costs are $200 and the variable costs are $13 per light. The software also projects that 20 lights can be sold each month if the price for a light is $40, and two more lights can be sold for each decrease of $1 in the price. Let x represent the number of lights produced and sold each month. (a) Determine the monthly cost Function C. C(x) = 13:: + 200 VI (b) Determine the monthly revenue function R. R(x) = (c) Determine the production level x that maximizes the monthly prot, assuming that 10 S x s 60. , sol lights need to be sold to maximize the prot. There is an absolute maximum prot of $l ' at X =| A graphing calculator is recommended. Financial planners at the Double D Corporation have determined that the cost to produce its Roxie eece boot and backpack combo can be modeled by C(x) = 0.07x3 2.2x2 + 73.13x + 104.26 0 S x S 55 where x represents the number of combos produced each clay and C(x) represents the daily cost in dollars. (a) Determine the average cost function AC. AC[X} = (b) Determine the daily production level x that minimizes the average cost. (Round your answer to the nearest whole number.) The average cost is a minimum when \\: units are produced. (c) Determine the average cost and total cost at the production level found in part (b). (Round your answers to two decimal places.) when E units are produced, the total cost is $ E and the average cost is $ E per unit. Determine the absolute extrema of the function on the indicated interval. f(x) = x3 - 3x2; [-1, 3] absolute minimum (x, y) = 2. - 4 (smaller x-value) X absolute minimum (x, y ) = -1, - 4 (larger x-value) X absolute maximum (x, y) = 0.0 (smaller x-value) absolute maximum (x, y) =( 3.0 (larger x-value)