Suppose you want to solve the following LP: maxcTx: Ax≤b, but unfortunately it is infeasible (think e.g. about an inventory problem where the demand cannot be satisfied by the warehouse). Let A ∈ Rm×n. Now suppose you can “augment” your LP by buying some more slack in your problem (think e.g. of buying some of the product from other warehouses). In particular, for i = 1, . . . , m, if you want to increase the right-hand side of the i-th constraint by some value λi, you will pay diλi for some fixed number di. Suppose moreover that the right-hand side of the i-th constraint can be augmented by at most ki, for i = 1,...,m. How can you find the optimal augmentation, i.e. the one that maximizes the profit of the optimal solution of the augmented LP minus the cost for the augmentation?
Theory and Design for Mechanical Measurements
Measurement is a term that refers to analyzing a manufactured component regarding the degree of accuracy for dimensions, tolerances, geometric profile, roundness, flatness, smoothness, etc. Measurement always involves comparing the manufactured component or the prototype with a standard specimen whose dimensions and other parameters are assumed to be perfect and do not undergo changes with respect to time.Precisely in mechanical engineering the branch that deals with the application of scientific principles for measurements is known as metrology. The domain of metrology in general deals with various measurements like mechanical, chemical, thermodynamic, physical, and biological measurements. In mechanical engineering, the measurements are limited to mechanical specific such as length, mass, surface profile, flatness, roundness, viscosity, heat transfer, etc.
Basic principles of engineering metrology
Metrology is described as the science of measurement, precision, and accuracy. In other words, it is a method of measurement based on units and predefined standards.
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