Use Application of Derivatives A wire of length L is to be cut into two pieces, one to form a square and the other to form an equilateral triangle. How should the wire be divided to maximize or to minimize the sum of the areas of the square and triangle?

Q: inventories

A: Given that : ABC produces and sells wooden desks. Company has 20 employees produces 30 desks in 1…

Q: 8. A truck is to be driven 135 km at a constant speed of x km/hr. Speed laws require that 50<x<100.…

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Q: Temperature between fluids in a heat exchanger used to heat a medium Based on the difference (X) (X>…

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Q: The total cost of producing x units of a certain commodity is c(x) thousand dollars, where: C(x)=x3…

A: Average cost function

Q: 10. We are going to fence in a rectangular field. Starting at the bottom of the field and moving…

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Q: (iv): A rectangular sheet of metal 360mm by 240mm has four equal squares cut out at the corners. The…

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Q: A rectangular box with volume 182 cubic feet is built with a square base and top. The cost is $1.50…

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Q: The demand for a certain company's e-reader can be approximated by 780 - 1 million units per year…

A: given: qd=780/p-1 qs=0.0195p-1

Q: The demand function for an office supply company's line of plastic rulers is p=0.85- 0.000459q,…

A: p=0.85-0.000459q Now total revenue is, R=price×quantity⇒R=0.85-0.000459q·q⇒R=0.85q-0.000459q2 Now…

Q: Find two positive numbers that satisfy the given requirements. The second number is the reciprocal…

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Q: The demand function for a tablet is given by the model p = 200-16x2  where p is measured in dollars…

A: Our objective is to Derive the number of tablets that the company could sell to make the same amount…

Q: y = 1.2889x3 - 358.53x2 + 48536x - 34188 What is the second derivative, what is the point of…

A: we have been given an equation  y=1.2889x3-358.53x2+48536x-34188 to find the inflection point we…

Q: open box is to be constructed so that the length of the base is 2 times larger than the width of the…

A: We will find the dimensions of the box.

Q: 3.4 Applied Optimization Activity 3.4.3. A hiker starting at a point P on a straight road walks east…

A: Given query is to find the distance of point z from p to minimize the time.

Q: The sum of two numbers is 8. Find the numbers if the sum of their cubes is to be minimal. The

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Q: A plant produces and sells semiconductor devices. The cost per one unit (also known as the unit…

A: Consider is the income from the sale of units manufactured during a month.

Q: The profit function for a certain commodity is P(x) = 190x - x2 - 1000. Find the level of production…

A: Given: The profit function for a commodity is Px=190x-x2-1000, Here P is expressed in dollars. On…

Q: Water is running into a hemispherical bowl having a radius of 10 cm at a constant rate of 3 cu.…

A: Hemispherical bowl radius= 10 cmdvdt=3 cu.cm/mindxdt=0.0149 cm/min

Q: x maximum point of y х — 2 4, - 2/2 0,0 03 - 3 2 4, 2/2

A: To find: The maximum point of y2=x2x-2. Concept used: Consider the point  x=c is a critical point of…

Q: Differenciate and simplify where its possible

A: We have to differentiate the following -  ddx1x2+x+13

Q: A company has started selling a new type of s tphone at the price of $110-0.05x where x is the…

A: Use the relation Profit = Revenue - Cost to write the equation. The revenue of x number of mobiles…

Q: A developer is planning a fence around a rectangular field. They are using three different types of…

A: The cost of fencing(per meter) on the: North side: $50 South side: $70 Other sides: $100. The…

Q: An offshore oil well is located in the ocean at point W, which is 5 miles from the closest…

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Q: The profit function for an operation is given by P(x, y) = 2200 + 24x − x^2 + 80y − y^2 where x is…

A: Optimization problem can be solved using the constraints provided in the problem. Equation of a…

Q: Write the application of Deravative" Linear approximation" also explain in detail with example.…

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Q: The demand function for a product is modeled by p(x) = 50e -0.0000125x where pis the price per unit…

A: Given demand function is p(x)=50e-0.0000125x. Obtain the revenue function.…

Q: A company can produce between 400 and 1000 items per day. The average cost per item is given by:…

A: Given, ACx=x3-13x2+40x+1000 Differentiating the given function with respect to x.…

Q: world price determined after trade? • How do you demonstrate gains from trade? • What are the key…

A: The Heckscher-Ohlin model incorporates a number of realistic characteristics of production from the…

Q: The total revenue function for a certain product is given by R= 870x dollars, and the total cost…

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Q: Find the maximum profit and the number of units that must be produced and sold in order to yield the…

A: For the given revenue and cost function, we need to find the maximum profit. Rx=50x-0.1x2,…

Q: The growth rate of the speed of sound in relation to the temperature in degrees Fahrenheit is a…

A: Let t be the temperature in degrees Fahrenheit, and yt be the speed of sound. First find the linear…

Q: 4. A farmer wants to build a fence in the configuration shown, with a total area of 3000 square…

A: We have to minimize C

Q: 6x – 2x and the x-axis into two There is a line through the origin that divides the region bounded…

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Q: Suppose a company has a fixed cost of $300 and a variable cost per unit of 3/4x+1460, where x is the…

A: Solution

Q: Budek is flying a kite. The kite is initially directly over her head at a height of 30 m. Then the…

A: The height of the kite is 30 m above the head. The kite is carried by the wind in the one direction…

Q: a.Find the profit function. b.Find the number of units that gives maximum profit. c.Find the maximum…

A: Given that: R( x) = 490 x dollars C (x) = 15000 + 30 x + x 2  dollars  where x is the number of…

Q: A firm has an average cost function A(q)=125q+q216−4. where q is the firm′s output. Determine the…

A: Given the average cost function, Aq=125q+q216-4 (1) To determine the level of output for average…

Q: The total revenue function for a certain product is given by R= 480x dollars, and the total cost…

A: Revenue R(x) = 480x Total cost C(x) = 15,000 + 40x + x2

Q: 3. A line of negative slope through (1, 2) cuts off a triangle in the first quadrant. For which such…

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Q: Average cost If the total cost function for a lamp is C (x) = 250 + 33x + 0,1x2 dollars, producing…

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Q: We are going to fence in a rectangular field that encloses 200 m2. If the cost of the material for…

A: We are going to fence in a rectangular field that encloses 200 m2. If the cost of the material for…

Q: A firm produces a product that has the production cost function C(x) = 420x + 14,420 and the revenue…

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Q: 1+ cost -dt = со 1- cost True

A: We are asked to find given statement is correct or wrong

Q: A closed box with a square base is to be constructed. The top and sides will be made of material…

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Q: Find two positive numbers that satisfy the given requirements. The second number is the reciprocal…

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Q: A piece of land next to a stream is to be divided into three adjacent fields and then fenced so that…

A: One side is covered with stream and not needed any fencing. Total area to be fenced is 800 ft².…

Q: 12. A 250 cm piece of wire is cut into two pieces. One piece is bent into an equilateral triangle…

A: Given, A  250 cm piece is cut into two pieces and the pieces is bent in equilateral triangle and…

Q: A company has started selling a new type of smartphone at the price of $110-0.05x where x is the…

A: Given that: Selling price of each smartpohne=$110-0.05xCost of parts for each smartphone =$ 50Labor…

Q: Suppose a company has a fixed cost of $300 and a variable cost per unit of 3/4x+1460, where x is the…

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