By Andrew B. Templeman (auth.)
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5 units. 4. A type 1 element may be produced either on line 1 at an extra cost of 500 units which, when added to the material cost of 650 units, gives a total cost of 1150 units or on line 2 at an extra cost of 1000 units giving a total cost of 1650 units. For type 2 elements the total costs are 1200 units per element if produced on line 1 and 1450 units per element if produced on line 2. 5 units if produced on line 3. The selling prices of a11 units are given in the problem and this now enables a profit to be calculated for each element produced on each line as follows.
21 2! (7 - 2)! - 2! 5! So the example problem has 21 possible vertices, each ofwhich is evaluated by solving two simultaneous equations. This presents quite a formidable task if all possible vertices are to be calculated. 5, the vertex formed by constraints gl and g3' If all twenty-one possible vertices are evaluated the next step must be to check whether each vertex is feasible or infeasible. 27 and if the vertex point violates any of the seven constraints it must be discarded as infeasible.
One problem involves equalities in the relationships among variables, the other two involve inequalities. These differences turn out to be very minor ones which are completely overwhelmed by the strong similarities among all three problems. The three physical problems of earthmoving, planning the production of a precasting plant and the plastic design of a portal frame structure at first sight appear to be totally different and to have nothing in common. One might have been excused for believing that they were all 'one-off problems, each requiring its own specific solution technique.