Optimization Problem: Q: What is the largest possible volume of an open vox that you can built from a fixed amount of paper (say 1000 square inches), if the length of the base is 3 times the width?

Q: An open-top box is to be made from a 20 in by 30 in piece of cardboard by removing a square from…

A: Let each side of the square cut-off from each corner be x in. then the length of the base of the box…

Q: 5. Find the dimensions of the rectangle in the figure shown below that will give the maximum…

A: let's assume length of rectangle is yfeet now, equating perimeterP of given figure with 12feet so,…

Q: A local station television is faced with a problem. It found that program A with 20 min of music and…

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Q: Suppose you are building boxes. Each box has a square base, and is 40 cubic inches in volume. The…

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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: 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: An open-top box is to be constructed so that its base is twice as long as it is wide. Its volume is…

A: Volume of cuboid is V=LWH Here,  L=lengthW=widthH=height Surface area of cuboid with open top is…

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

A: Given query is to find the way of fency to minimize the cost.

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: I need help with optimization problems. For example, a rectangular pasture has to have 20,000 square…

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Q: You are building a right-angled triangular flower garden along a stream. The fencing of the left…

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Q: 2. A rancher from above needs two equal adjacent rectangular pens that share a fence in the middle.…

A: Given that ,Rancher needs two equal adjacent rectangular pens with a fence in middle. this can be as…

Q: 2. Suppose a wire three feet log is to be cut into two pieces, with each piece to be formed into a…

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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 company sells square carpets for $5 per square foot. It has a simplified manufacturing process for…

A: Given: Cost per square foot of carpet is $5 Let the length of the carpet be x feet. Side of each…

Q: An open-topped storage box with a square base has a capacity of 5 m3. The material for the sides…

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Q: You are building a right-angled triangular flower garden along a stream as shown in the figure. The…

A: Given:- You are building a right-angled triangular flower garden along a stream as shown in the…

Q: A student is about to take a test that contains computation problems worth 7 points each and word…

A: A student is about to take a test that contains computation problems worth 7 points each and a word…

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: ) Amran is constructing a rectangular box with a square base and an open top. The box must have a…

A: Let the side of the box be x cm and the height of the box is h cm Therefore, the volume of the box…

Q: 1. Angelo, who is in a rowboat 2 kilometers from a straight shoreline wishes to go back to his…

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

Q: 13. A rectangular dog pen of 800 sq. feet is to be constructed as shown. The cost is $5 per running…

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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: Solve the following problems 1. An open box is to be made from a square piece of aluminum, 3 cm. on…

A: To find: The maximum volume of the box. Given: The side of square piece is 3 cm. Formula used: The…

Q: Solve the following problems involving optimization. 2. Find a pair of non-negative number that…

A: We have to find a pair of non-negative number that have a product of 162 andhave to minimize the sum…

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

A: I use second derivative test to find out dimensions where amount of required fencing minimum

Q: Solve the following problems. a. A door is being built and the bottom is a rectangle and the top is…

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

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Q: 2. Find two positive numbers whose product is 750 and for which the sum of one and 10 times the…

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

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Q: 2. Suppose a wire three feet log is to be cut into two pieces, with each piece to be formed into a…

A: 2) as per our norms we have to write one question at a time kindly repost remaining questions.

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

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

A: given ,  measure of cardboard , length =32 inches   and   breadth = 20 inches

Q: Suppose we have 45 m² of material to build a box with a square bottom and no top. What dimensions…

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Q: Find the dimensions of a rectangle with perimeter 1000 meters so that the area of the rectangle is a…

A: Since you have posted multiple questions, as per our policy we will answer first question. Please…

Q: A rectangular corral of 600 square meters is to be fenced off and then divided by a fence into two…

A: Given the area of the rectangle.

Q: 1. Amazon wants to create an open-top box with a square bottom with only 149 in2 cardboard (the…

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Q: ) Ivan is laying out a page of a newspaper. He knows he needs to get 50 square inches of text on the…

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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: 4. Find two positive numbers whose product is 750 and for which the sum of one and 10 times the…

A: For minimum , second derivative of the function should  be positive.

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

A: Here we use the second derivative test to find the dimensions of the required box.

Q: fence is to be built to enclose a rectangular area of 280 square feet. The fence along three sides…

A: Rectangular area=280 square feet   Let the length of rectangle=x   Let the width of rectangle…

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

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

Q: Solve the following problems. 1. If the product of two consecutive odd integers is represented by y…

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

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Q: 3. Rae plans to build a rectangular pig pen against one of the walls of her barn. If she has 18…

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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.