# Chapter 4 - Self Study Solutions - Linear Programming...

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Linear Programming Applications in Marketing, Finance and Operations Management Chapter 4 Homework Solutions 11. Let xij= units of component ipurchased from supplier Min12x11+13x12+14x13+10x21+11x22+10x23s.t.x11+x12+x13=1000x21+x22+x23=800x11+x21600x12+x221000x13+x23800x11, x12, x13, x21, x22, x23j0
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17. a. Let FM = number of frames manufactured FP = number of frames purchased SM = number of supports manufactured SP = number of supports purchased TM = number of straps manufactured TP = number of straps purchased Min38FM+51FP+11.5SM+15SP+6.5TM+7.5TPs.t.3.5FM+1.3SM+0.8TM21,0002.2FM+1.7SM25,2003.1FM+2.6SM+1.7TM40,800FM+FP5,000SM+SP10,000TM+TP5,000FM, FP, SM, SP, TM, TP 0.
c. Subtract values of slack variables from minutes available to determine minutes used. Divide by 60 to determine hours of production time used. Constraint1Cutting:Slack = 0 350 hours used2Milling:(25200 - 9623) / 60 = 259.62 hours3Shaping:(40800 - 18300) / 60 = 375 hoursd. Nothing, there are already more hours available than are being used. e. Yes. The current purchase price is \$51.00 and the reduced cost of 3.577 indicates that for a purchase price below \$47.423 the solution may improve. Resolving with the coefficient of FP = 45 shows that 2714 frames should be purchased.
Linear Programming Applications in Marketing, Finance and Operations Management The optimal solution is as follows: OPTIMAL SOLUTION Objective Function Value = 361500.000 Variable Value Reduced Costs -------------- --------------- ------------------ FM 2285.714 0.000 FP 2714.286 0.000 SM 10000.000 0.000 SP 0.000 0.900 TM 0.000 0.600 TP 5000.000 0.000 Constraint Slack/Surplus Dual Prices -------------- --------------- ------------------ 1 0.000 2.000 2 3171.429 0.000 3 7714.286 0.000 4 0.000 -45.000 5 0.000 -14.100 6 0.000