Th Summer 2017 QM352-740 30 x Take a Test Mosab Alaskar x By system of equations

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Th Summer 2017 QM352-740 30 x Take a Test Mosab Alaskar x By system of equations I c Secure https://www.mathxl.com/Student/Player Test.aspx?testld-160945115 Summer 2017 QM352-740 Quantita Quiz: Mod B Quiz This Question: 15 pts 5 of 9 complete) Consider the following LP problem developed at Zafar Malik's Carbondale, Illinois, optical scanning firm: Maximize z 1x1 1x2 Subject to: 2X1 1x2 is 1000 (C1) 1x1 2x2 s 100 (C2) X1 X220 on the graph on right constraints C, and c2 have been plotted. a) Using the point drawing tool, plot all the comer points for the feasible area. The optimum solution is: x1 3333 (ound your response to two decimal places. x2 33.33 round your response to two decimal places). optimal solution value z (ound your response to two decimal places. b) If a technical breakthrough occurred that raised the profit per unit of x1 to $3, due to this change, the optimal solution stays the same As a result of the technical breakthrough, the optimum solution is: Click the graph, choose a tool in the palette and follow the instructions to create your graph. 888

Explanation / Answer

Part (a) is correct .

In part(b) when solution is changed when profit per unit is changed to $3 then profit = 3X1 + X2

so critical values here from the graph are A(50,0) , B(0,50) and C (33.33, 33.33)

so Total profit TP (A) = 3 * 50 + 1 * 0 = 150

TP(2) = 0 + 50 = 50

TP(3) = 3 * 33.33 + 33.33 = 133.33

so Maximum profit will CHANGE.

and X1 = 50 and X2 = 0

Optimal solution value Z = 150

(c) X1 profit only increases to $1.10 instead of $3 so profit = 1.1X1 + X2

so again critical point will be the same A(50,0) , B(0,50) and C (33.33, 33.33)

so TP(A) = 1.1 * 50 + 0 = 55

TP(B) = 1.1 * 0 + 50 = 50

TP(C) = 1.1 * 33.33 + 33.33 = 70

so optimal solution is Z = 70 here

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