Please explain in steps and number the each answer according to question.

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Maximize B = 4xy2, where x and y are positive numbers such that x+ y2 = 2. The maximum value of B is D. (Simplify your answer. Type an exact answer, using radicals as needed.) Minimize Q =5x2 + 4y, where x + y= 9. X= y= (Simplify your answer. Type an exact answer, using radicals as needed. Use integers or fractions for any numbers in the expression.)Raggs, Ltd. a clothing rm, determines that in order to sell x suits, the price per suit must be p = 200 - 0.5xt It also determines that the total cost of producing x suits is given by 000 = 4500 + 0.75x2. a) Find the total revenue, R(x). b) Find the total prot, P(x). c) How many suits must the company produce and sell in order to maximize prot? d) What is the maximum prot? e) What price per suit must be charged in order to maximize prot? a) R(x) = b) P(X) = c) suits d) The maximum prot is $ e) The price per unit must be $ A lifeguard needs to rope off a rectangular swimming area in front of Long Lake Beach, using 1600 yd of rope and oats. 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. A(x) = (Type an expression using x as the variable.) The length of the shorter side of the rectangular region is V The length of the longer side of the rectangular region is V The maximum area of the rectangular region is V A rectangular box with a volume of 612 ft3 is to be constructed with a square base and top. The cost per square foot for the bottom is 15, for the top is 10, and for the sides is 1.5. What dimensions will minimize the cost? What are the dimensions of the box? The length of one side of the base is l VI The height of the box is | VI (Round to one decimal place as needed.) dy Differentiate implicitly to find = 7xy +2 = 0 dy dxdy Differentiate implicitly to find . Then find the slope of the curve at the given point. y2 - x3 =9; (3, -6) dy dx The slope of the graph at the given point is (Type an integer or a simplified fraction.)Differentiate implicitly to find v. Then find the slope of the curve at the given point. 2x2 + 7xy +3y2+16y-8=0; (-2,0) dy dx The slope of the curve at the given point is (Type an integer or a simplified fraction.)