Question

Material science division of ABC Company needs circular metallic plates of diameters 3 cm and 6 cm to perform experiments on heat treatment studies. The requirement for these plates are 2500 and 1500 respectively. These are to be cut from parent metallic sheets of dimension 6×15 cm 2 . Formulate this as a linear programming problem so as to minimize the number of parent metallic sheets used.
Find out the number of basic solutions, feasible solutions, and basic feasible solutions for the above problem.

Answer 1

Answer:

Consider an LP in standard form: min{cTx:Ax=b,x≥0}.min{cTx:Ax=b,x≥0}. A feasible solution is any x≥0x≥0 such that Ax=bAx=b . Without loss of generality, we can assume that the m×nm×n matrix AA has full row rank, so AA has mm linearly independent columns. For some choice of mm linearly independent columns of AA called basic columns, a basic solution is any xx such that Ax=bAx=b and the n−mn−m nonbasic variables are all zero. The basic variables then must be xB=B−1bxB=B−1b where the columns of BB are the basic columns of AA . If in addition, x≥0,x≥0, then xx is a basic feasible solution.