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ABSTRACTThis paper generalizes the announced price increase problem to consider a variety of practical concerns arising out of applications ranging from foreign exchange fluctuations to upper limits on the purchase of discounted supermarket items. These include limitations on the amount that can be purchased at the old price and/or on the length of the grace period, within which buyers may take advantage of this lower price. These constraints give rise to 16 possible situations. For each situation purchasing and inventory decision rules are developed. A numerical example is discussed to highlight the main features of the models.

The interactions between electric and magnetic subsystems in a ferroelectric-ferromagnetic composite occur through mechanical forces. Here we discuss results of a systematic investigation on the strength of the magnetic response of the composite to an applied electric field, known as the converse magnetoelectric (CME) effect, and its dependence on the ferroic order parameters and volume fraction for the two phases. Studies were carried out on composites of lead zirconate titanate and 2-30-mu m-thick nickel zinc ferrite (NZFO) films grown by liquid phase epitaxy on lattice matched (100) and (111) MgO substrates. Ferromagnetic resonance was utilized to determine the strength of CME from data on electric field E induced shift in the resonance frequency and its dependence on ferrite film orientation and thickness as well as MgO substrate thickness. The CME coupling coefficient A was found to be a factor of 2 to 4 higher in samples with NZFO films with (100) orientation than for (111) films. A decrease in A was measured with increasing ferrite film thickness and a very significant enhancement in the strength of CME was measured for decreasing MgO thickness. A model for CME that takes into consideration the influence of nonferroic MgO substrate was developed, and estimated A values are in very good agreement with the data. The results presented here are also of importance for a new class of electric field tunable ferrite microwave devices. ; Public domain authored by a U.S. government employee