In order to treat a certain bacterial infection, a combination of two drugs is being tested. Studies have shown that the duration of the infection in laboratory tests can be modeled by D(x, y) = x² + 6y² – 18x 28y + 2xy + 160 where x is the dosage of the first drug and y is the dosage of the second drug (both in hundreds of milligrams). Find the amount of each drug necessary to minimize the duration of the infection. first drug hundred mg second drug hundred mg

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Q: The Builders Company can produce up to 200 tiles per week. If the weekly cost function is…

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

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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: A manufacturer has determined that the total cost C of operating a factory is C = 0.5x2 + 15x + 5000…

A:

Q: The production function for a firm is p(x, y) = 96x"y"", where x and y are the number of units of…

A: P(x,y)=96x34.y14 Labor cost =$144 Capital cost =$1875 cost =144x+1875y

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

A: To find the number of units that should be produced at each location to minimize the cost.

Q: Solve  max f( x,y , z) 3x2+y problem by means of Lagrange multipliers under the constraints of…

A:

Q: Show that the problem B symmetric minimize || B A ll subject to Be R is solved by A + AT B= %3D

A: To show that the problem minimizeB∈ℝn×n∥B-A∥F subject to B being symmetric is solved by B=A+AT2

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 pencil cup with a capacity of 36 square inches is to be constructed in the shape of a rectangular…

A: Use application of derivative to find dimensions of the cup to minimize construction cost.

Q: Find the values of (Xx) that minimize the function f(x,y) = 8x²- xy + 12y² subject to the constraint…

A: (a)

Q: Find the point on the graph of y = 1x that is closest to the point (2, 0). [Hint: 2(x - 2)2 + y2 has…

A: Given: y=x Let the point closest to (2,0) be P(x,y). Distance between point P(x,y) and (2,0) is:…

Q: A box with a rectangular base is to be constructed of material costing $2/square inches for the…

A: Given problem is : A box with a rectangular base is to be constructed of material costing $2/square…

Q: The total cost to hand-produce x large dolls and y small dolls is given by C(x,v) = 2x2 + 4y2 + 4xy…

A: To find x and y that minimizes cost

Q: A manufacturer's total cost equation per day is given by the equation TC = 440 + 4q +,0001Q². If…

A: Given: TC=440+4q+0001Q2 To find: Solution

Q: find the values of  x greater than or equal to 0 y greater than or equal to 0 that maximize…

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Q: A firm has two plants, X and Y. Suppose that the cost of producing x units at plant X is x^2 + 12000…

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Q: A one-product firm estimates that its daily total cost function (in suitable units) is C(x) = x3 -…

A: Given that, Cost function = C(x) = x3-6x2+13x+15 Revenue function = R(x) = 28x Then the profit…

Q: Consider the problem f (x) subject to g;(x) = 0, minimize %3D

A: Given, the problem                 minimise f(x)            subject to   gi(x)=0, i=1, . . ., l…

Q: A company needs to manufacture cylindrical cans out of tin, each of which must have both a bottom…

A: Solve by minimizing surface area

Q: A consumer has $280 to spend on two commodities, the first of which costs $2 per unit and the second…

A:

Q: Suppose the labor cost (in dollars) for manufacturing a particular product can be approximated by…

A: Given that the labor cost is approximated by the function Lx,y=32x2+y2-8x-6y-2xy+197.Here x is…

Q: 4. Find the orthogonal trajectories of the family of parabola described by the equation (y– 3) = Cx.…

A: The solution of the problem is given in the next step.

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 firm has two plants, X and Y. Suppose that the cost of producing x units at plant X is  x2 + 600…

A: Given, cost of producing x units at X plant = x2+600 cost of producing y units at Y plant = 3y2+1400…

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

A: Let the size of pool, x×y=xy=1000 Let the sides of the pool be x, x, y  and also length of Infinity…

Q: A manufacturer has determined that the total cost C of operating a factory is C = 0.5x² + 15 + 5000…

A: Given cost function is C=0.5x2+15x+5000 The average cost per unit is given by…

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

A:

Q: Emily is making a closed rectangular box with a square base from two different woods. The wood for…

A: The solver program in the Excel can be used to optimize a function within specific constraints. The…

Q: A visitor is staying in a cottage that is 10 miles east of the closest point on a shoreline to an…

A: Given A visitor is staying in a cottage that is 10 miles east of the closest point on a shoreline to…

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: C(x, y, z) = 90 + 6x + 4y + z where x is the cost of 1 pound of one raw material, y is the cost of 1…

A:

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

A:

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

A:

Q: In order to treat a certain bacterial infection, a combination of two drugs is being tested. Studies…

A:

Q: Suppose the labor cost (in dollars) for manufacturing a camera can be approximated by  L(x,y)=…

A:

Q: A manufacturer has determined that the total cost C of operating a factory is C = 2x + 60x + 200,…

A:

Q: Solve the LP problem. If no optim Minimize c = x + y subject to x+3y2 8 3x + y2 8 x2 0, y 2 0. 3つ =…

A:

Q: Suppose the labor cost (in dollars) for manufacturing a camera can be approximated by L(x,y)=…

A: Given :Lx,y=32x2+y2-3x-6y-2xy+101

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: Use the simplex method to minimize  w=3y1+2y2 subject to:  2y1+3y2>=60 y1+4y2>=40 with…

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Q: Minimize Z=8x+12y subject to 4x+6y214, 4x+5y9, x>0, y20 M=?

A: Given LPP is Minimize  Z = 8x + 12y Subject to  4x + 6y ≥ 14, 4x + 5y ≥ 9, x ≥ 0, y ≥ 0

Q: A boat is located 3 km in the ocean from a point, says P on a straight shoreline. That point is 5 km…

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Q: The amount of space required by a particular firm is f(x, y) = 1000(6x2 + y2)^1/2, where x and y…

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Q: The production function for a firm is p(x, y) = 96x"y"", where x and y are the number of units of…

A: We will use Lagranges multiplier method to find optimal solution  To maximize/ minimize f(x,y,z)…

Q: Find two numbers x and y with x-y = 20 for which the term xy is minimized.

A: In this problem, we have to find the two numbers "x and y"

Q: The maximum value of f(x,y) = x +y subject to xy = 16 (using method of Lagrange multipliers) is 16

A: Given function is f(x,y)=x+y  Constraint: xy=16

Q: Two machines, A and B produce items at the rate of 50 units per hour and 40 units per hour j.…

A:

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.