Lecture1

extwtor palm us 1 ton of a and 2 tons o b some

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Unformatted text preview: income produced by sale of a unit of each type of paint is different - Ext~Ior Patm Is sold a~ wkot&e for S3000 I ton l l l - Intwlor Paint IS cold for S2OOtl I ton l - lntcrlor Palm usea 2 tons o( A and 1 ton of B l The availability of each Raw Material is Limited - Up to 6 ton, per day of A Is svailabk The demand limits for each type of paint are known from market surveys - Dally d.mand for imwtor cannot ba mom than 1 ton p., day 0v.r the demand for WdWfor - Drt,y d.mmd fo, ,m.rto, cmno( excnd 2 tOn¶ p.r dry - Up to 8 tons par day of 8 IS avaIlable Constraints Decision Variables There are only 2 decision variables which are under management’s control, which are defined as follows: .Q +2x, 6 6 (Limit on Material B) x, - .rh I 1 XE = Amount ot‘Estenor Paint (in Tons) the J, 52 cornpan! produces per da! and I, = Amount &hit on Material A) 2.~~ +_r, < 8 XEJ, 20 of intenor Pamt (III Tons) the (E..cess of Id. over Ext.) (Demand for Interior) (Nonnegat~vitl\ Constraints) compan! produces per da! Objective Function l l l The Complete Model The objective function relates the inputs (decision variables) to the objective variable (usually denoted as 2) The goal is to optimize z - in this case to Maximize the gross income (in thousands) t&\unze 2 = 3.~~ + Zs, The objective function in this problem is: mawmize ,? = 3x, +2x, subject to xp +2x, 5 6 2x, + .I, 5 8 I, - xc 5 1 x, I2 XE..Y, 2 0 .- EM-602 I QM-710 (NJ) Lecture 1 Page l-5 x, A convex set Xl x1 A concave set fbaoiblo Solution spew far hint w ‘- Possible Sites of Ootimal Solution .- x2 t IsoObjective Line MAxz=c1ul+c2~ Ioaobjoatin Linr laa0M at ho Origin (03) \ EM-602 I IaoObjooti~ QM-710 (NJ) Lecture 1 Page l-6 l.inO 5 x2 t IroObjoch Line begina to arit the Faadbla kaa EM-602 I QM-710 (NJ) Lecture 1 Page l-7 --...
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