Average Cost A manufacturer has determined that the total cost C of operating a factory is C = 0.5x + 15x + 5000 where x is the number of units produced. At what level of production will the average cost per unit be minimized? (The average cost per unit is C/x.)

Q: Example: Use quadratic interpolation with three points method to find the position of the minimizer…

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Q: Exercise 3 (Finding a Cost Function). A company produces a product for which the marginal cost of…

A: Given Data: The marginal cost function is: dCdx=2x-12 The fixed cost is: F=$125 (3a) The total cost…

Q: 62. Production Level Suppose c(x) = x³ – 20x2 + 20,000x is the cost of manufacturing x items. Find a…

A: Cx=x3-20x2+20000x The average cost function is, Ax=Cxx=x3-20x2+20000xx=x2-20x+20000 Now…

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Q: 26. Minimizing Average Cost Suppose c(x) = xe" – 2x², where x is measured in thousands of units. Is…

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Q: A rectangular storage tank with an open top is to have volume (20 m). The length of the base is…

A: Given that:

Q: The cost, in dollars, of producing z units of a certain item is given by C (z) = 5z – 8/I – 3. Find…

A: Since you have asked multiple questions in a single request, we would be answering only the first…

Q: Absolute extrema on open and/or unbounded regions Rectangular boxes with a volume of 10 m3 are made…

A: Concept: The base must be in any case be square, because a square has a maximum area at minimum…

Q: Using simplex method determine the optimal solution. Given: Minimize Cost= 6x + 16y Subject to:…

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Q: A silo is to be built with a vertical cylindrical tube with no bottom but topped by a hemispherical…

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Q: An open-top box is to have a square base and a volume of 10 m3 . The cost per square meter of…

A: Given: Volume of an open-top box with a square base = 10 m3, The cost per square meter of material…

Q: Analysis of daily output of a factory during a 8-hour shift shows that the hourly number of units y…

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Q: The cost, in dollars, of producing x units of a certain item is given by C (x) = 10x – 8/a – 7. Find…

A: By using formula of average cost function and concept of minimized the function

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A: Basic logic and modelling of the problem can be used to solve the question. Rate of fuel consumption…

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Q: 33. Cost A manufacturer has an order for 1000 units of fine paper that can be produced at two…

A: Given data:- Order value of fine paper = 1000 units Produced at two location, x1 & x2 The cost…

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Q: Upgrading a highway A highway must be constructed to con- nect Village A with Village B. There is a…

A: Here we find the minimize cost.

Q: Minimizing Packaging Costs A rectangular box is to have a square base and a volume of 45 ft. If the…

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Q: The cost, in dollars, of producing x units of a certain item is given by C (x) = 20x – 4/x – 3. Find…

A: The Cost of producing x units of a certain item is given by: C(x)=20x-4x-3

Q: Given the cost function C(x) = 120 - 10x +x %3D 1. Find the minimum cost. II. II. Find the Average…

A: Here is the Answer and Exp

Q: Shipping crates A square-based, box-shaped shipping crate isdesigned to have a volume of 16 ft3. The…

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Q: A rectangular storage tank with an open top is to have volume (20 m). The length of the base is…

A: Given that the volume of the container is 20m3 i.e. Volume = 20 m3 Material cost of base = $20 m2…

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A: The situation is illustrated as shown in the figure below: Here, the objective is to find the…

Q: Minimum Area A rectangular poster is to contain 648 square inches of print. The margins at the top…

A: Given,   A rectangular poster is to contain 648 square inches of print.    The margins at the top…

Q: The total cost for a manufacturing company is C(q)=1/30 q^3-3/10 q^2+q, where q is the quantity of…

A: Let us assume a function f(x). For the function f(x), the rate of change of function is given by the…

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Q: A rectangular storage tank with an open top is to have volume (20 m). The length of the base is…

A:

Q: Laying cable An island is 3.5 mi from the nearest point on a straight shoreline; that point is 8 mi…

A: For minimize the value we use differentiation.

Q: price p (in doi equation q = 800- 20p and 0s ps 40 (i) Express the revenue R as a function of q.…

A: Given demand equation is q=800-2pand 0≤p≤40where p is the price and q is the quantity sold

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Q: A box with a square base and open top must have a volume of 4000 cm°. We wish to find the dimensions…

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Q: The average cost per hour in dollars of producing x riding lawn mowers iIs given by the 2200 C(x) =…

A: To find out the minimum average cost using graphing utility.

Q: A rectangular storage tank with an open top is to have volume (20 m'). The length of the base is…

A: Given:

Q: Cut out squares (of the same size) from the four corners of a square cardboard of given side length…

A: The side of the square = L  let the length of the square = x,

Q: 2. Design the optimal cylindrical container that is open at one end and has walls of negligible…

A: Consider the given diagram, The the area of the cylinder will be, A=πr2+2πrh The volume of the…

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Q: Rectangular boxes with a volume of 8 m³ are to be made of three materials. The material for the top…

A: Let the dimensions of the box be x,y, and z. Given the volume of the rectangular box is xyz=8. Let…

Q: QI/ A box with rectangular sides was designed from a metal to occupies a 25 m³ of a material. If the…

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Q: Minimizing Packaging Costs A rectangular box is to have a square base and a volume of 24 ft³. If the…

A: In order to minimize the cost of packaging, the surface area should be minimum possible. Here the…

Q: box with length equal to " x " times the width must have a volume of " V " cm3. Find the dimensions…

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Q: box with length equal to " x " times the width must have a volume of " V " cm3. Find the dimensions…

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Q: The cost, in dollars, of producing z units of a certain item is given by C (z) – 5z - 6/= – 6. Find…

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Q: The cost per unit C, in dollars, of producing off-road 4x4 ATV at a local manufacturing plant is…

A: ∙ If f(x) = ax+bx+c  ,  the f is minimum    when x = -b2a and minimum value is f-b2a∙ Let f(x) be a…

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Q: Maximum Profit A corporation manufactures digital cameras at two locations. The cost of producing x,…

A: Given: Cost of producing x1 units Cost of producing x2 units Profit function is

Q: Total Cost is given by C(x)=3x^2+20x +4800. Find the x value that minimizes average Cost.   b. How…

A: Given informationTotal cost is given as

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: