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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A farmer has 100 acres of available land and $20,000 to spend. He wants to plant the combination of crops which maximizes his profit. Complete parts (a) through (c). Profits and Constraints for Crops Corn Cabbage Potatoes Total Number of Acres X3 $224 $90 X1 X2 100 Cost (per acre) Profit (per acre) $320 $128 $20,000 $180 $60 %3D Maximize subject to: y1 +320y2 2 y, + 128y2 2 Y1 +224y2 2 Y, 20, Y2 20 with (Simplify your answers. Do not factor.) (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 90 acres but capital increases to $21,000. The farmer's estimated profit is $ (Type an integer or a decimal.) (c) Suppose the farmer has 110 acres of land but only $19,000. Find the optimum profit and the planting strategy that will produce this profit. Planting acres of potatoes, acres of corm, and acres of cabbage will produce an optimal profit of $ (Type integers or decimals.)
In detail
Minimise x2+y−2xyx2+y−2xy subject to the constraint y=1
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.
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
A petroleum refiner se

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