Quantitative Methods

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7-1 Discuss the similarities and differences between minimization and rnaxirnization problenrs using thc graphical solution approaches of LP.

":-2 lt is intportant to understand the assumptions un- derlying the use of any quantitative analysis model. What are the ptions and requi fbr an LP nrodel to be lated and used?

7-3 It has been said th hLPp that has a 7-ll A linear program ha\a miximum proiit of $600. fcasiblc region l'ras an Explain.

ol'solutions. One constraint in this lc:m is 4X + 2Y = 80.

7-,1 You have just I'ormulated a zation LP prob- lcm and are pt"eparing tcr ically. What

criteria should you con in deci would be casier t.o solvc ploblcm by point method or the t line approach?

7-5 Under what condition it possible lirr an LP prob- lcm to havc morc orlc optimal solution'l

7-6 Develop your owlr cqualities and usc

of constraint equations and in- to illustratc graphically cach

of the following

(a) an unbounded problem (b) an infeasible problem (c) a problcm containing rcdundant constraints

The protluction manager of a large Cincinnati manufacturi-ng lirm once nrilde the statement' 1-l? Explain how a change in a technological coellicicnt

can atTect a problem's optimal solution. How can a

change in resource availability affect a solution'l "l would lik[ to use LP. but /'s a technique that opcrat.s urrd\ c,rrrditi,,ns / cr'rtainly. My plant docsn't have th\t ctrtaint/it's a world of uncer- tainty. S,r LP crn\ bc u..'/hcrc." Do you thirrk this

in why the manager

7-10 A linear program has the objective of maxtmtz- ing protit : 12X + 8I. The nraxirnum profit is $8,000. [.Ising a computer vr.'e find the upper bound for prolit on X is 20 and the lower bound is 9. Dis- cuss the chanses to thc optimal solgtion (thc valucscuss the changes tct thc opttmal st)|4tl(rn (thc valucs

,,f the valirhlcs\nd rhe pl olitt tffit would (reuur il' \

thc profit on Xw\t'increased.,{o $l-5. How would the optirnal solutio\ change if the profit on X werc incrcased to S25 .' \

7-7

Maximize profit : subject to

1-9

stafemcnt has anY

may have said it.

7-8 'fhe mathcmatical ionships that follow were lornrulated bv an ions research analyst at the

7-1.1 Thc Electrocomp Corporalion manulactures twcr electrical products: air conditioners and large fans. The asse rnbly pr'ocess lor each is similar in that bolh require a certain amount of wiring and drilling. Eactr

air conclitioner takes 3 hours of wiring and 2 hours ol ilriltin-e. Each fan must -qo through 2 hours

of wirin-q

antl I httul ol drilling. During thc next prodttction period, 2zl0 hours ol wiring time are available ancl up to 1.10 hours of drilling tirne may be usec1. Each air conditioner sold yields a profit o{'$25. Each {an

asserr.rblcd may be sold for a !i15 prot'it. Formulate and solve this LP production mix situation to find the best combination of air conditioners and fans that yields the liighest profit. Use the corncr point graphical approach.

7-15 Electrocomp's management realizes that it lbrgot to include two critical constraints (see Problern 7-14). In palticular, Inaniigclnent dccides that thcre should be a minimum number of air conditioners produccd

Smith-Lawton invalid for use an LP

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Discuss the role of sensitivity analysis in LP. Llnder what circunrstances is it needed. and under what conditions rlo you think it is noL necessary'l

Note: meals the problent tlay be solved with QM lor Willdows; means the prohlenr rnirv be

solved with Ercel; and nteans the problem may be solved with QM tirrWindows andlor Excel.

lrand 'ide ol cach of l our consl\inls.

(b) Explain .the si-enificance of tN technological coel-ticients.

(c) Solve iour problem graphically to find the opti- nral yblution.

1tl1 Illu/tratc glaphically thc c{'tbct of ir.rcrcasing thc contribution rate o1'youl first variahle (X1) by 50% ovcr the value you first assigned it. Does this change the optirnal solution?

euantitative Analygs for Managenefi, Twelfth Edition, by Barry Render, Ralph M. Stair, Michael E. Hanna, and Trevor S. Hale- Published by Prentic€ Hall'

Copyright @ 2015 by Pearson Education, lnc.

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