22-20-18-16-14-12-10-BO8-6-4-2-0P.2..4.6-810 12XJ14 1618 20 22C L.P. Model:MaximizeSubject to:Z=1X+10Y4X+3Y $36.2X+4Y ≤ 401Y26X,Y 201.) Plot and label the constraints C₁, C₂ and C3 (using the line drawing tool) on the provided graph2.) Using the point drawing tool, plot the point that maximizes the objective function.The optimum solution is:(C₁)(C₂)(C3)X=Y =Optimal solution value Z =(round your response to two decimal places).(round your response to two decimal places).(round your response to two decimal places).

Answered: Image /qna-images/answer/8f03e037-ffbd-4908-94a9-c93ea4578d6e.jpg

Answered: L.P. Model: Maximize Subject to: Z= 1X…

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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You are given the following variables: • B = Batman Comics • S = Superman Comics Income = 10B + 5S %3D %3D The feasible region is shaded. At what values does the graph reach the maximum income? 10+ 9- 6 7 8 9 1 Batman Comics Answer: The maximum Income is 20 and occurs when: Batman Comics =0 and Superman Comics = 2 sungtman Comies 4.
(FAB 4) Use Lagrange Multipliers to find the maximum and minimum values of f (x, y) = 81x² + yšubject to the constraint 4x2 + y? = 9
K b. Consider the following constrained maximization problem: The objective function is: f(x,y) = x Maximize the objective function subject to the constraint: 2x + 9y = 396 What is the slope of the level set of the objective function? (This is a fraction with an integer times y over an integer times x. The value in the numerator is negative.) 6 11 What is the slope of the constraint line? (This is negative and a fraction with no variables.) What is the relationship between x and y? (The answer is a fraction.) y=x What are the optimal values of x and y? irrect: 0
In detail
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?
K Find the minimum and maximum values of z = 5x + 2y, if possible, for the following set of constraints. 4x+6y 2 24 x+6y ≥ 12 x>0, y20 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The minimum value is (Round to the nearest tenth as needed.) B. There is no minimum value.
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.
Determine the amount of slack or surplus for each constraint. If required, round your answers to one decimal place. (1) A + 4B ≤ 21 (2) 2A + B ≥ 7 (3) 3A + 1.5B ≤ 21 (4) -2A + 6B ≥ 0
Jim's Camera shop sells two high-end cameras, the Sky Eagle and Horizon. The demands and selling prices for these two cameras are as follows. Ds = demand for the Sky Eagle Ps= selling price of the Sky Eagle DH = demand for the Horizon PH = selling price of the Horizon Revenue Ds = 223 - 0.60PS + 0.35PH DH= = 265 + 0.10Ps - 0.64PH The store wishes to determine the selling price that maximizes revenue for these two products. Develop the revenue function R (in terms of P and PH only) for these two models, and find the revenue maximizing prices (in dollars). (Round your answers to two decimal places.) Price for Sky Eagle Price for Horizon Optimal revenue R = Ps (223 -0.60P+ 0.35P₁ +PH (265 +0.10P - 0.64P н' Ps = $309.24 = $ 315.75 H R = $77244.46 xxx

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