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1. Alifeguard needs to rope off a rectangular swimming area in front of Long Lake Beach, using 500 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.) 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. av)=[ (Type an expression using x as the variable.) The length of the shorter side of the rectangular region is ema Tea| (1) The length of the longer side of the rectangular region is ee ee (2) The maximum area of the rectangular region is ee (3) $$____ (1) ya. (2) ya. (3) a. ya. ya', yd', O ya*. O yd. O yd. ID: 3.5.15-Gl Awaste management company is designing a rectangular construction dumpster that will be twice as long as it is wide and must hold 22 yd of debris. Find the dimensions of the 7 dumpster that will minimize its surface area. 7 x Write the surface area formula in terms of the width, x. Assume the dumpster has an open top. The width of the dumpsteris[____| (1) The length of the dumpster is [J @ The height of the dumpster is aes | (3) (Round to the nearest hundredth as needed.) (1) O ya. (2) O ya. (3) O yd. O ya. O yd". O ya'. O ya?. O ya'. O yd?. ID: 3.5.23-Gl 3. Find the maximum profit and the number of units that must be produced and sold in order to yield the maximum profit. Assume that revenue, R(x), and cost, C(x), are in thousands of dollars, and x is in thousands of units. R(x) =7x 2x2, C(x) =x? - 3x? +3x +1 The production level for the maximum profit is about el units. (Do not round until the final answer. Then round to the whole number as needed.) The profit is about ee | (Do not round until the final answer. Then round to the whole number as needed.) ID: 3.5.29-BE