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1 Individual problem 5 Yorkville University BUSI 2013 Business Decision Analysis
2 Problem 2. Let: X = units of production 1 produced Y = units of production 2 produced Max 30x + 15Y X + 0.35y <=100 0.3X + 0.2Y <= 36 0.2X + 0.5Y <= 50 X,Y >= 0 X + 0.35y <=100 X = 100 Y = 285.71 0.3X + 0.2Y <= 36 X = 120 Y = 180 0.2X + 0.5Y <= 50 X = 250 Y = 100 Max = 30x + 15Y 30(77.894) + 15(63.157) =2,336.84 + 947.355 = 3284.20 Figure 1 X + 0.35y <=100 0.3X + 0.2Y <= 36 (3.33) X + 2/3y = 120 Y = 63.157 X + 0.35 = 100 X + 0.35(=63.15789) = 100 X + 22.10526 = 100 X = 77.894 Optimal (77.894, 63.157)
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4 28.Let G = Invested in growth stock S = Income stock fund M = Money market fund Max = 0.20G+0.10S+0.06M S.t. Max. Risk 0.1G+0.05S+0.01M <= (0.05) (300,000) Growth fund Min >= (0.1) (300,000) Income Fund >= (0.1) (300,000) Money market fund >= (0.2) (300,000) So, the, G, S, M>=0 Variable Value cost G 1,20,000 0 S 30,000 0 M 150,000 0 Constraint Slack/surplus Dual prices 1 0 1.556 2 90,000 0 3 0 -0.022 4 90,000 0 5 0 0.044 C. Growth fund =< 0.15 – 0.6 Income fund =< 0 – 0.122 Money market fund =< 0.02 – 0.2 D. Increasing the risk index to 0.06, mean 0.01 increase over previous index of 0.05. This would result in increase of 3000 points (=0.01*300000) in the right-hand side of constraint 1. 4668 in yield (=1.556*3000). 1 st Constraint of dual price is 1.556 provides this information
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