For the given maximization problem, (a) determine the number of slack variablesneeded, (b) name them, and (c) use slack variables to convert each constraintinto a linear equation.Maximizez = 9x, + 3x2 +X35x, + 4x2 + 8x3s 1635x, + 6x2 + 13×3 s 211subject to:a. How many slack variables are needed?withX1 20, X2 20,X3 20

A maximization problem is given. We need to find number of slack variable and name them. Also, we…

Answered: For the given maximization problem, (a)…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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2. Solve by Lagrange Multiplier Method: Clearly identify your constraint function and your system. You may use either approach you learned in class and on the video. Mr. Eppolito has S360 to spend on fencing to fence a rectangular garden. The fencing for the north and south sides of the garden costs $10/ft. The fencing for the east and west sides costs $15/ft. Find the dimensions that will allow Mr. Eppolito to fence in the largest-sized garden. Draw a diagram of this scenario. Write the method you will use to solve it, then do so, showing all the necessary equations.
3. Solve by Lagrange Multiplier Method: Clearly identify your constraint function and your system. You may use either approach you learned in class and on the video. The annual production of skateboards at a local factory is described by the equation: U (x,y) = 800x(1/4) y(3/4) where x is worker-hours and y is capital expenditure (measured in units of $10 dollars). Manufacturing costs the factory roughly 10x + 20y dollars. a) What values of x and y will allow the factory to maximize the production of skateboards while spending only $600?
1. Maximization Model. Answer in complete solution.
Develop your own set of constraints, at least three equations and/or inequalities, and use them to illustrate graphically each of the following conditions: 1. an unbounded problem
A company produces two types of solar panels per year: x thousand of type A and y thousand of type B. The revenue and cost equations, in millions of dollars, for the year are given as follows. R(x,y) = 6x + 8y C(x,y)=x²-3xy + 6y² + 3x + 5y − Determine how many of each type of solar panel should be produced per year to maximize profit.
Please refer to the picture for questions a, b, c, d. Thank you so much.
A farmer has 500 acres of available land and $100,000 to spend. He wants to plant the combination of crops which maximizes his profit. Complete parts (a) through (c). Profits and Constraints for Crops Potatoes Corn Number of Acres Cost (per acre) Profit (per acre) X₁ $320 $120 with Minimize subject to: y₁ +320y₂ 2 120. Y₁+1282 2 40 w = 500 y₁ + 100000 ₂ Y₁+224y > 60 Y₁ 20, y₂ 20 $128 $40 The farmer's estimated profit is $ (Simplity your answer.) Cabbage X3 $224 $60 S ≤ = Total 500 $100,000 Z (b) The solution to the dual problem can be interpreted as shadow profits. Use shadow profits to estimate the farmer's profit if land is cut to 400 acres but capital increases to $110,000.
find the maximum value of p=10x+15y+26 given the following constraints: y-x<=1

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