I need help with optimization problems. For example, a rectangular pasture has to have 20,000 square feet, it is alongside a river so it doesn't need a fence on that one side. What would the demensions be that require the least amount of fencing?

Q: What is the minimum product you can achieve from two real numbers, if one of them is three less than…

A: This question is based on application of derivative.

Q: Find the objective function in the given problem (in terms of w) if the constraint is that the sum…

A: Note: Please provide complete instructions for first problem. Given  The box has a sum of length,…

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: A rectangular box with a closed top is being designed. The material for the top and bottom costs 60…

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Q: Find two real numbers whose difference is 40 and whose product is a minimum.

A: Let the two real numbers be x & y. Since the difference is 40, therefore x-y=40⇒y=x-40   →1 Now…

Q: Where is optimization often applied and what is its importance?

A: Solution:Optimization:Optimization methods are used in many areas of study to find solutions that…

Q: You want to build a 1100 square foot rectangular infinity pool. Three of the sides will have regular…

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Q: A farmer needs to put in a fence in their rectangular field. If we look at the field from above, the…

A: Given that the fencing of the field for east side and west side are $10/feet , cost of the south…

Q: You are building an open-top aquarium with a square base with side length x ft. Material for the…

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Q: A playground with a rectangle shape with a 500 m^2 area is to be surrounded by a fence, with an…

A: topic - optimization

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

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

Q: You want to build a 1000 square foot rectangular infinity pool. Three of the sides will have regular…

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Q: A wire 16 feet long has to be formed into a rectangle. What dimensions should the rectangle have to…

A: Given: Length of the wire = 16 feet Assumptions: Let x, y be the length and width of the rectangle…

Q: Solve the optimization problem. Minimize F = 3x2 + 3y2 with xy2 = = 16. F =

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Q: Find two positive numbers whose product is 100 and whose sum is a minimum. (This is optimization…

A: Let's assume two positive numbers are a and b Now, We know that for two positive numbers a+b2≥ab…

Q: A circuit board manufacturer estimates the yearly demand to be 1,000,000. It costs $200 to set up…

A: Given data: Estimated yearly demand=1,000,000 Setup cost = $200 Manufacturing cost=$10 Storage…

Q: An ice cream company is designing fancy glass containers for their ice cream. The containers will be…

A: Please see the explanation below

Q: Suppose that a homeowner wants to create a rectangular enclosure for his pet turkey in his backyard…

A: It is given that, the rectangle has one side of enclosure and fencing on other 3 sides. A total of…

Q: A rectangular poster is to contain 800 square inches of print. The margins at the top and bottom of…

A: Given data: Area of the poster which contains print is: A = 800 in2 Margin at top and bottom is: x0…

Q: Your new puppy needs a rectangular dog run outside . You have 50 feet of fencing and plan to use the…

A: To maximize the area , we use Lagrange multipliers.

Q: A rectangular garden with an area of 500 yards is to be enclosed by a fence, and an additional fence…

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Q: What is the minimum value of 3x 4x +1 and for what value of x does it occur?

A: We have to find the minimum value of 3x2-4x+1 and for what value of x does it occur.

Q: You want to build a 1200 square foot rectangular infinity pool. Three of the sides will have regular…

A: Area of rectangular infinity pool is 1200 square foot. Cost of regular pool wall is $12 per foot,…

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

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Q: In a world where people's happiness is the product of the square of the amount of one's food which…

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Q: a closed rectangular box is made with two kinds of materials. the top and bottom are made of thick…

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Q: 2. A management company is going to build a new apartment complex. They know that if the complex…

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Q: Find two numbers whose difference is 6 such that the sum of their squares is a minimum.

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Q: You have a wire of length 2 m, which you can bend either into a square or a circle. You also have…

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Q: Answer the optimization problems sytematically: A closed box with a square base is to have a volume…

A: Given: Closed box with a square base is to have a volume of 2000 cm2The material for the top and…

Q: The guild leader of an adventurer group decides to construct a rectangular wall around their base…

A: Here we solve the given problem of calculus.

Q: A company manufactures two types of bicycles, a racing bicycle and a mountain bicycle. The total…

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Q: A closed rectangular box is made with two kinds of materials. The top and bottom are made with…

A:

Q: This is a linear algebra/optimization problem:

A: Given,             f(x→)=2x+y  and     h→(x)→=x+y+zx2+z2 Where   x→=xyz   and  Minimize f(x→)…

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: A farmer has 800 meters of fencing and needs to fence off a rectangular paddock that borders a…

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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…

A:

Q: Mr. Sample wants you to draw a picture on a piece of paper with 2 inch margins and 1 inch margins on…

A: The objective is to find the length and width of paper.

Q: You want to build a 1100 square foot rectangular infinity pool. Three of the sides will have regular…

A:

Q: A Norman window is a rectangle with a semicircle on top. Suppose that the perimeter of a particular…

A: Let, x denotes the half width of the rectangle.y denotes the height of the rectangle.And…

Q: A farmer, well versed in traditional optimization problems, has decided to buy a rectangular plot of…

A: A rectangular plot of 200 square meters of land on the bank of a river, and surround it on three…

Q: Suppose that C(x)=x² – 30x+15000 is the average cost of manufacturing x items. Find a production…

A:

Q: A management company is going to build a new apartment complex. They know that if the complex…

A: To find the number of apartments for which the cost is minimum and also find the minimum cost.

Q: A management company is going to build a new apartment complex. They know that if the complex…

A:

Q: You want to build a 1100 square foot rectangular infinity pool. Three of the sides will have regular…

A: Given problem:- You want to build a 1100 square foot rectangular infinity pool. Three of the sides…

Q: An aquarium is to be constructed to hold 2160 in The base is to made of slate and the sides of…

A:

Q: Find the dimensions of the rectangular box with largest volume such that the sum of the lengths of…

A: Consider the provided question, Let the dimensions of the rectangular box are x, y, z.

Q: You want to build a 1200 square foot rectangular infinity pool. Three of the sides will have regular…

A:

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.