A piece of wire of length 58 is​ cut, and the resulting two pieces are formed to make a circle and a square. Where should the wire be cut to​ (a) minimize and​ (b) maximize the combined area of the circle and the​ square?

Q: 5. A piece of wire is with a length of 4 m is cut into two pieces, and the resulting two pieces are…

A: Let the length of the wire cut=xAll sides of square are same side length=yPerimeter= 4 y…

Q: 5. Use Lagrange multipliers to determine the dimensions of a rectangular box, open at the top,…

A:

Q: a. A rectangular pen is built with one side against a barn. If 1500 m of fencing are used for the…

A: Note:- As per our guidelines, we'll answer the first one as both are different question. Please…

Q: A manufacturer has determined that the total cost C of operating a factory is C = 0.5x2 + 15x + 5000…

A:

Q: 1. A cable wire 100 meters long is to be cut into two pieces. One of the pieces will be bent into…

A: Let length of one part is x  Therefore length of another part is (100-x)

Q: 3] Use Lagrange multiplier to find the dimensions that will maximize the area for rectangle whose…

A:

Q: Of all numbers whose sum is 50, find the two that have the maximum product. That is, maximize Q =…

A:

Q: a. A rectangular pen is built with one side against a barn. If 1500 m of fencing are used for the…

A: a. Let the dimensions of the pen be x m and y m.  Now, the length of the perimeter to be covered by…

Q: Show that the problem B symmetric minimize || B A ll subject to Be R is solved by A + AT B= %3D

A: To show that the problem minimizeB∈ℝn×n∥B-A∥F subject to B being symmetric is solved by B=A+AT2

Q: Find the number in the interval [ – 1, - 0.25] so that the sum of that number and its square is…

A:

Q: Where should he cut the wire so that the sum of the areas of the square and the circle is maximized?

A:

Q: Of all numbers whose sum is 46, find the two that have the maximum product. That is, maximize Q = xy…

A: Given ,           x+y=46           Maximize , Q=xy

Q: Consider a wire 4 ft long cut into two pieces. One piece forms a circle with radius r and the other…

A:

Q: A piece of wire of length 61 is cut into two pieces. One piece is bent into a square and the other…

A:

Q: 4.1- You are building five identical pens adjacent to each other with a total area of 1000 m², as…

A: Given, Five identical pens are given below.

Q: If an isosceles triangle has perimeter P, how long must the legs of the triangle be to maximize its…

A:

Q: 3] Use Lagrange multiplier to find the dimensions that will maximize the area for rectangle whose…

A: Using Lagrange multiplier to find the dimension of rectangle whose area is maximum

Q: A box with a rectangular base is to be constructed of material costing $2/square inches for the…

A: Given problem is : A box with a rectangular base is to be constructed of material costing $2/square…

Q: A customer has made a request for a wooden box with an open top that needs to have a volume of…

A: Note:- As per your demand we solve it for only constraints for this optimization  Given problem:- A…

Q: Of all numbers whose sum is 52, find the two that have the maximum product. That is, maximize Q = xy…

A: Given, Q=xy                        ...(1) Where x+y=52⇒y=52-x                            ...(2)

Q: The upper right-hand corner of a piece of paper, 15 in. by 4 in., as in the figure, is folded over…

A:

Q: a. A rectangular pen is built with one side against a barn. If 300 m of fencing are used for the…

A: a) Let x represents the width of the pen and y represents the length of the pen. Given that, the…

Q: e) A farmer wishes to enclose three pens with fencing, as shown. If the farmer has 700 feet of…

A: 700 feet of fencing to work .

Q: A pentagon is formed by placing an isosceles triangle on a rectangle, as shown in the figure. II the…

A: The given a pentagon is formed by placing an isosceles triangle on a rectangle, as shown in the…

Q: The upper right-hand corner of a piece of paper, 15 in. by 8 in., as in the figure, is folded over…

A: Concept used: If f''x>0 if and only if fx is the absolute minimum value, where f'x=0.…

Q: Solve the following LP graphically: maximize 13x1 + 23x2 subjected to 5x1 + 15x2 0.

A:

Q: Suppose the feasi ble region has four corners, at points (0, 0), (4, 0), (0, 3), and (3, 2) If the…

A: Given corner points of the feasible region are

Q: Find two positive integers such that their sum is 10, and minimize the sum of squares.

A: Given  two positive integers such that their sum is 10, To minimize the sum of squares

Q: A first class radio-telephone operator wishes to cut the wire 100 meters long into two pieces. One…

A:

Q: You are designing a rectangular poster to contain 75 in? of printing with a 3-in margin at the top…

A:

Q: The upper right-hand corner of a piece of paper, 12 in. by8 in., as in the figure, is folded over to…

A:

Q: 5. Crunchy Coco Hunks cereal comes in a rectangular box that must be exactly 4 inches deep. If the…

A:

Q: 17. Find two positive integers such that their sum is 10 and maximize and minimize the sum of their…

A:

Q: A box (with no top) is to be constructed from a piece of cardboard with sides of length A and B by…

A:

Q: a. A rectangular pen is built with one side against a barn. If 300 m of fencing are used for the…

A: a. Let the width of the pen be x ft.  So, length is y=300-2x feet. Then, the area of the pen is,…

Q: A farmer wants to construct a fence around an area of 7776 square feet in a rectangular field and…

A:

Q: A boat is located 3 km in the ocean from a point, says P on a straight shoreline. That point is 5 km…

A:

Q: 2. A rectangular area is enclosed with fencing on three sides, with the fourth side along a house.…

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: A piece of wire of length 60 is cut, and the resulting two pieces are formed to make a circle and…

A: Let x be the length of the wire cut for the circle then the length of the wire cut for the square.If…

Q: What necessary conditions are replaced by "minimize"? obeyed by a solution to (1) if "maximize" were

A: To write the  necessary condition for min ∫t0t1F(t,x(t),x'(t))dt with x(t0)=x0

Q: The area of a rectangle is A = LW. If three sides of the rectangle are fixed, 2W + L = 40, what are…

A: "Since you have asked multiple question, we will solve the first question for you.If you want any…

Q: Find a pair of non-negative numbers that have a product of 162 and minimize the sum of two times the…

A: Let the numbers be x,y. Given  x·y=162y=162x The function to be minimized will be Fx=2x+y…

Q: a. A rectangular pen is built with one side against a barn. If 1200 m of fencing are used for the…

A:

Q: Two chicken coops are to be built adjacent to one another from 144 ft of fencing. Part: 0/ 2 Part 1…

A: Two chicken coops are to be built adjacent to one another from 144 ft of fencing To find dimensions…

Q: The upper right-hand corner of a piece of paper, 12 in. by 8 in., as in the figure, is folded over…

A:

Q: A piece of wire of length 69 is cut into two pieces. One piece is bent into a square and the other…

A: Here we have to find the length of the square and circle such that the sum of areas of  square and…

Q: Consider two nonnegative numbers x and y such that x+y=10. Maximize and minimize

A:

Q: A rectangular building covering 6,000m2 is to be built on a lot as shown in the figure. If the…

A: Minimize area