Quantitative Business Analysis 2022

Quantitative Business
Analysis
[DATE]

Problem 7.28
(a) Optimal solution change
Maximize profit=$ 3 X + $ 2Y
Subject to constraints
2 X +Y ≤150
2 X +3 Y ≤300
Graph
Intersection point D
2 X +Y ≤150
2 X +3 Y ≤300
X =37.5 ,Y =75 (Optimal solution)
Maximum (37.5, 75) = 3 *37.5 + 2*75 = 262.5 (Optimal solution)
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When profit per unit of changes to $4.50
Maximum profit = $4.5 X + $2 Y
In this case, the slope of iso-profit line would change.
Maximum (75,0) = 4.5*75 + 2*0 = 337.5(Optimal solution)
(b) Profit per unit Y changes to $3
Maximum profit = $3X + $3Y
Maximum (37.5, 75) = 3 *37.5 +3*75 = 337.5
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