) t.) Uonslder the tollowrng lrnear programrnrng prolrl

) t.) Uonslder the tollowrng lrnear programrnrng prolrlem: NIin 11111 I 2t18 * 5116 l74r2a 1lrzn l Trzc + 15z3a + 6z3c suDlecl lo: r7A+rrBl116-3 :x2A+r2Blr2c-1 r3glrg6:3 rrA+ r2A i r3a -3 :LIB+t2B:2 r1C+r2C!136:) ri; /0 i-123 j: A BC (a) Show that this linea.r programming problem can be thought of as a transportation problem. Draw the associated network. (b) Suppose r1Ar1B)r2Br3Ar3c are the basic variables. Find the associated ba.sic solution. Is it feasible? Is it optimai? Justify. If the given basic solution is not optimal firrd an optirnal solutiori. . (c) Find an optimal solution to the dual of the given network flow problcrn. (d) Does the given (primal) problem have a unique optirnal solution? Ifnoi find all optimal solutions. (e) What is the range of c16 (wliich is currently 5) for which ihe solution found in part (b) remains optimal? (f) Suppose we increase the right hand side of the second a.nd slrth constraints by 1 so that we now require 223 I rzn ttzC -2 ancl rtC IrzcIrzC:3 Will the optimal cost increase or decrease? By how much?
3. (25 points) Consider ihe following integer programming problem: Max 1311 f 822 subject to: 11+2r2

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