09 QM Lecture Note C Supplement Ans Key

09 QM Lecture Note C Supplement Ans Key - d SP for Market...

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E: # of external modems to be produced I: # of internal modems to be produced Max(Total revenue) Max $45 E + $ 120 I Engineer A: 20 E + 5 I <= 2400 minutes Engineer B: 15 E + 30 I <= 2400 minutes Demand for E: E <= 100 units Demand for I: I <= 50 units Questions: (i)Which is the preferred product now, E or I, why? Substituting E=100, I=50 for the EngineerA and B constraint equations, confirm that Eng B is bottleneck. Bang for buck: E: $45/15=$3< $120/30=$4= Bang for buck for I Prefer I. What is the optimal E= (2400-50*30)/15= 60 units I=……. .50 units (ii) a)Allowable increase for the objective coefficient of E= 60-45=$15; X/15>=$4 or X>= $60, b)Allowable decrease for the objective coefficient of I=120-90=$30; Y/30<=$3, Y<= $90 c) SP for Engineer B=$3 Additional 15 minutes will change the total revenue by $45, sp=$45/15=$3
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Unformatted text preview: d) SP for Market for E=$0 e) SP for Market for I=$30 One additional unit of demand for I brings in $120, but need to reduce two units of E, losing $90, net change =$30, sp=30/1=30 f) Suppose the shadow prices are Engineer A: 20 E + 5 I <= 2400 minutes $0/min Engineer B: 15 E + 30 I <= 2400 minutes $3/min Demand for E: E <= 100 units $0/unit Demand for I: I <= 50 units $30/unit Compute the “MC” E =$45 Reduced cost for E:$0 Compute “MC” I =$120 Reduced cost for I:$0 h) To produce or not to produce a new product, Wireless modem? Assume, no cannibalization. The new product W needs 10 min from A, 10 minutes from B, and sells for $45/unit. Should we produce W? MC for W=$30 < MR=$45, Produce W....
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This note was uploaded on 08/10/2011 for the course BUSQOM 0050 taught by Professor Glowackia during the Spring '08 term at Pittsburgh.

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09 QM Lecture Note C Supplement Ans Key - d SP for Market...

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