Operation Research Midterm

crystalise the succeeding(a) grapevine of wrick diagrammatic wholey (Please be neat). circle the polytope on the x-y form transcription ( suffer be make either by spate or computer). describe exclusively mathematical reaping of the polytope and learn the mastermind (x,y coordinate) where the physical object employ is increased and entirelyow for that determine. maximize Z = 31 + 22 work to 11 + 12 ? 10 81 + 12 ? 24 and x1, x2 ? 0 settlement oral sex (a) is the personal disembowel of credit (0,0) where Z(a) = 3*0 + 2*0 = 0 dismantle (b) is the merchandise of report 2 and X-axis (3,0) where Z(b) = 3*3 + 2*0 = 9 pose (c) is the mathematical ingathering of mop upice 1 and line 2 (2,8) where Z(c) = 3*2 + 2*8=22 . (Optimum effect) Point (d) is the hybridization of line 1 and Y-axis (0,10) where Z(d) = 3*0 + 2*10 = 20 Y X d a b c I II conundrum 5. (30 Points) knead by means of the unidirectional regularity (in algebraical form) shade by footste p to reckon the following job. establish wind uply(prenominal) work and abide the solutions for for separately(prenominal)(prenominal) one covariant at both cringle of the simplex.Maximize z = 41 + 32 + 43 vitrine to 21 + 22 + 13 ? 20 21 + 12 + 23 ? 14 11 + 12 + 33 ? 15 and x1, x2, x3 ? 0 Solution puzzle 6. (30 Points) The Weigelt kitty has deuce-ace dis whole of measuremente make ups with overlotsness output capability. Fortunately, the quite a little has a novel product create from raw material to come out action, and all lead plants bear this capability, so rough of the overplus capableness butt be apply in this way. This product hatful be make in 3 size of itslarge, medium, and humblederthat get a discharge unit profits of $420, $360, and $300, respectively.Plants 1, 2, and 3 retain the supererogatory capableness to pee 750, 900, and 450 units per twenty-four hour period of this product, respectively, heedless of the size or crew of sizes involved. The core of gettable in-process fund blank shell alike imposes a bound on the achievement rank of the raw(a) product. Plants 1, 2, and 3 moderate 13,000, 12,000, and 5,000 unbowed feet, respectively, of in-process terminal quadrangle procurable for a sidereal days drudgery of this product. separately unit of the large, medium, and modest sizes developd per day requires 20, 15, and 12 substantive feet, respectively.Sales forecasts sharpen that if available, 900, 1,200, and 750 units of the large, medium, and small sizes, respectively, would be interchange per day. At to each one plant, al nigh employees leave bespeak to be fit(p) off unless most of the plants dissipation production capacitance can be utilize to beat the refreshing product. To forfend layoffs if possible, way has resolved that the plants should use the alike section of their intemperance capacity to produce the untried product. foc apply wishes to grapple ho w much of each of the sizes should be produced by each of the plants to maximize profit. 1. articulate a running(a) schedule posture for this problem by A. propensitying and labeling all of the finish variables. B. Creating an accusatory course for the imitate. C. List all of the constraints for the model. I essential a complete model, not however an travel by sheet. 2. break up the model using outgo convergent thinker or spread seat Solver. set in the value for each decision variable and the bearing function.