MGMT 651_hw 4_soln_2020.docx - MGMT 651 u2013 Analytics...

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MGMT 651 – Analytics for Managerial Decision-Making Homework 4 Solutions Worth 100 points 1. (25 points) Chapter 3 Problem 30 a. Let L = minutes devoted to local news N = minutes devoted to national news W = minutes devoted to weather S = minutes devoted to sports MIN 300L+200N+100W+100S S.T. 1) 1L+1N+1W+1S=20 (Time available) 2) 1L>3 (15% local) 3) 1L+1N>10 (50% requirement) 4) 1W-1S<0 (Weather - sports) 5) -1L-1N+1S<0 (Sports requirement) 6) 1W>4 (20% weather) OPTIMAL SOLUTION Objective Function Value = 3300.000 Variable Value Reduced Costs -------------- --------------- ------------------ L 3.000 0.000 N 7.000 0.000 W 5.000 0.000 S 5.000 0.000 Optimal Solution obtained using MS: L = 3, N = 7, W = 5, S = 5 ; Total cost = $3,300 . Constraint Slack/Surplus Dual Prices -------------- --------------- ------------------ 1 0.000 -100.000 2 0.000 -100.000 3 0.000 -100.000 4 0.000 0.000 5 5.000 0.000 6 1.000 0.000 OBJECTIVE COEFFICIENT RANGES Variable Lower Limit Current Value Upper Limit ------------ --------------- --------------- --------------- L 200.000 300.000 No Upper Limit N 100.000 200.000 300.000 W No Lower Limit 100.000 100.000 S 100.000 100.000 300.000 RIGHT HAND SIDE RANGES Constraint Lower Limit Current Value Upper Limit Submit your homework as one single attachment. Include POM-QM input and output screenshots wherever applicable. Accepted files types are . doc .docx .epub .gdoc .odt .ott .oth .pdf .rtf (PDF preferred) 1 of 6
------------ --------------- --------------- --------------- 1 18.000 20.000 30.000 2 0.000 3.000 10.000 3 6.667 10.000 12.000 4 -2.000 0.000 10.000 5 -5.000 0.000 No Upper Limit 6 No Lower Limit 4.000 5.000 b. Each additional minute of broadcast time increases cost by $100 (dual price is negative); conversely, each minute reduced will decrease cost by $100. These interpretations are valid for increase up to 10 minutes and decreases up to 2 minutes from the current level of 20 minutes.

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