Example 6: A farmer in Ontario has 100 hectares which he wishes to fence as a rectangular field subdivided into two smaller fields with a fence parallel to one of the sides. What should the dimensiong be that will minimize the cost of the fencing?

Q: 15. You want to put a fence around a rectangular field and then subdivide the field into 4 smaller…

A: Let's find.

Q: A rectangular plot of farmland will be bounded on one side by a river and on the other three sides…

A: Maximization problem using derivative

Q: Please

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Q: A piece of wire of length 58 is​ cut, and the resulting two pieces are formed to make a circle and a…

A: Let the circle gets x units and the square gets (58-x) units x is from 0 to 58   Let radius of the…

Q: A manufacturer has determined that the total cost C of operating a factory is C = 2.5x2 + 75x +…

A: Given  Cx = 2.5x2+75x+25000

Q: The cost of building an office complex, x floors high, in a prime location in Accra is made up of…

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Q: Suppose that a company needs 1,800,000 items during a year and that preparation for each production…

A:

Q: Suppose a company's profits are given by P = x^2 y, where x is the amount of money they spend on TV…

A: given  P = x^2 y x+y=12

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: A rectangular corral of 726 square meters is to be fenced off and then divided by a fence into two​…

A: Given problem is : A rectangular corral of 726 square meters is to be fenced off and then divided…

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: a. A rectangular pen is built with one side against a barn. If 1400 m of fencing are used for the…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: 3. Suppose that the revenue in selling a tables is equal to 200x -0.25x² dollars, and producing a…

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Q: A manufacturer has determined that the total cost C of operating a factory is C = 2.5x2 + 75x +…

A:

Q: A closed rectangular box with a square base and a volume of 12 cubic feet is to be constructed from…

A: Volume=12 cubic feet Top is made of a metal costing $2/ft2 Remainder of wood costing $1/ft2

Q: . A rectangular pen is built with one side against a barn. If 1400 m of fencing are used for the…

A: l+2w=1400; l=1400-2w; l=2(700-w); are=lw ; so, lw=2(700-w)w =(1400w-2w^2);  to maximize,…

Q: a. A rectangular pen is built with one side against a barn. If 1700 m of fencing are used for the…

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Q: 5. A farmer wants to fence an area of 9600 square feet in a rectangular field and then divide it in…

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Q: (b) A wire of length 100 centimeters is cut into two pieces. One piece is bent to form a square. The…

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Q: A company needs 450,000 items per year. Production costs are 500$ to prepare for a production run…

A: Let the number of items in each production be  Therefore, Number of production  Total storage cost…

Q: A supermarket manager estimates that a total of 400 cases of soup will be sold at a steady rate…

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Q: Suppose that a company needs 1,800,000 items during a year and that preparation for each production…

A:

Q: A rectangular pen is built with one side against a barn. If 1800 m of fencing are used for the other…

A: a) Assume that the length of the pen be x and width be y. Since the length of fencing on three sides…

Q: A rectangular pen is built with one side against a barn. If 1600m of fencing are used for the other…

A: a) Let the two parallel sides are x m and the third side= y m  So the total fence needed= 2x+y=1600…

Q: Farmer Brown wants to fence in a rectangular plot in a large field, using a rock wall which is…

A: Please see the diagram below to comprehend the situation. East and West dimension is y and the…

Q: -2 Albert wants to make an open box from a rectangular piece of cardboard by cutting squares out of…

A: We have to find the following.  Let the side of cutting square be x

Q: why minimize ||A x – b|| + A ||x|| and minimize ||A x – b||² + A ||x||2 are the same?

A: Consider the terms of the given function one by one Now the given function of x gives always the…

Q: a. If she walks at 3 mi/hr and rows at 2 mi/hr, at which point on the shore should she land to…

A: Given: A boat on the ocean is 4 mi from the nearest point on a straight shoreline; that point is 6…

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

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Q: A piece of wire 28 m long is cut into two pieces. One piece is bent into a square and the other is…

A:

Q: Suppose that a company needs 1,800,000 items during a year and that preparation for each production…

A: The preparation for production costs $500. The cost of producing 1 item is $24 to produce each item…

Q: Applied Optimization Problem 1. You need to construct a fence around an area of 1600 ft. What are…

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Q: A farmer wishers to fence off three identical adjoining rectangular pens, each with 300 square feet…

A: Given, Cost of the fence of outer boundary of the pens = $3 per foot Cost of the fence of two…

Q: 13. A farmer wants to fence in an area of 1.5 million square feet in a rectangular field and then…

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Q: A farmer wants to make three identical rectangular enclosures along a straight river, as in the…

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Q: Find the minimum Cost of C(x) = 24x^2 - 820x.

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Q: Suppose that a company needs 1,200,000 items during a year and that preparation for each production…

A: Consider the provided statement. The preparation for production costs $500. The cost of producing…

Q: Suppose a manufacturer has determined that the total cost C of operating a factory is C =0.4x² + 17x…

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. A rectangular pen is built with one side against a barn. If 2500 m of fencing are used for the…

A: Part (a) The diagram of the field is shown below. Given that, the total length of fencing is 2500…

Q: A rectangular field with one side along a river is to be fenced. Suppose that no fence is needed…

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Q: Bob wants to create two pens, as shown in the figure. One pen is for a garden and it needs a heavy…

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Q: me of 485 cubic meters. The cost per square meter of materials is $2,000 for the ceiling, $9,000 for…

A: INTRODUCTION: Let z=f(x,y) be the function of x and y, the extrema of the function is dependent on…

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. A rectangular pen is built with one side against a barn. If 1400 m of fencing are used for the…

A: Note: Since you have posted multiple questions we will solve the first question for you. If you want…

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

A:

Q: Suppose that a company needs 1,500,000 items during a year and that preparation for each production…

A: Solution

Q: 16. A farmer wants to fence an area of 2 million square feet in a rectangular field and then divide…

A: Here first we find the total length of fence in terms of the sides. Now using differentiation we…

Q: A farmer wants to fence an area of 6 million square feet in a rectangular field and then divide it…

A: