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# page%20231 - Suppose that the current basis remains optimal...

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Unformatted text preview: Suppose that the current basis remains optimal as we ittct“asc the rightmhand side of" the ith constraint of an LP by A In. (A h, a: 0 means that we are decreasing the rightd-tz-tnd side ol‘ the ith constraint.) Then each unit by wltieh Constraint t‘s right—hand side is in~ creased will increase the optimal :—value (for a max problem) by the shadow price. Thus. the new optimal zmvalue is given by {New optimal :wvalue) : (old optimal :— *alue) it (Constraint is shadow price} Ah; {‘2} For a ininimixalion problem. {New optimal :«value) : (old optimal :-value) * (Ctnistraint E‘s shadow price} Ah, {2] For example. it 95 carpentry hours are n railable. then at}: : 15, and the new :-~value is given by New optimal :mvaluc : itil) + lﬁtl) : Slilﬁ .y We will continue our discussion oi" shadow prices in Sections 5.2 and 5.3. importance of Sensitivity Anaiysis Sensitivity analysis is important for several reasons. in many apptications. the values ol‘ an LP"s parameters may change. For example. the prices at which soldiers and trains are sold or the availability ol‘ carpentry and ﬁnishing hours may change. ll" a parameter changes. then sensitivity analysis often makes it unnecessary to solve the problem again. For example. it‘the proﬁt ctmtribut‘ion ol‘a soldier increased to \$3.50. we would not have to solve the (iiiapetto problem again. because the current solution remains optimal. ()l‘ course. solving the ("riapetto problem again would not be much work. but solving. an Lil" with thousands of" 'at'iables and constraints again would be a chore. A knowledge ol‘senm sitivity analysis often enables th- analyst to determine from the original solution how changes in an {P‘s parameters change its optimal soiution. Re ‘all that we may be uncertain about the values of parameters in an LP. For exam— ple. we might be uncertain about the weekly demand for soldiers. With the graphical method. it can be shown that il‘ the weekly demand for soldiers is at least 20. then the 0p" titnztl solution to the Ciiapetto problem is stiil (20. 60) (see Problem 3 at the end of" this section). Thus. even it“ Giapetto is uncertain about the demand for soldiers. the company can be Fairly conlitlent that it is still optimal to produce 2t.) soldiers and (it) trains. hat it" the contribution to proﬁt for trains is 4 For the Dorian Auto problem (Example 2 in Chapter 3). n .‘slotl and ft}. the current basis remains optnnai. [t 3 Find the range ol‘ values on the cost o'l‘a CLH‘ncdy ad in“. antribution to profit for trains is \$2.50. then what would ﬁe ‘ l g . , for which the current basis remains optimal. --1_ new optima so Litton‘; it Find the range oi‘values on the cost ota tootbnll ad how that if available carpentry hours remain between lot which the current basis t‘ei‘nains optimal. ad ltlt). the current basis remains Optimali- ”V bell-WT“ I: Find the range ot‘vuhies tor required i-th eXbosures ltlt) carpentry hours are attainable. would (.iiapetto it); which the current basis remains optimai. Determine White 29 soldiers and (it) trains? the new optimal soiution if}? -i- A million l-llW expo~ iron that il‘ the weekly demand for solczliers is at least sures ”"6 “lull-“L hen the current basis ren‘iains optimal. and (.iiapetto ‘1 Find “‘0 muse “Willie?" {03‘ I‘Cllllll'ﬂi HIM CKlm-‘iill‘CS Ulcl till protlttee 20 soldiers and ()0 traihs_ for which the current. basis remains optitnai. Determine 5. ’t tEratihEral lntrutluctiun tn Sensitiiitt analysis ...
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