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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