Discover for Yourself: An Optimal Control Model in Insect Colonies

Winkel, Brian

doi:10.1080/10511970.2012.753965

Cited by 2 publications

(1 citation statement)

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“…Stated another way, we seek an advertising function u(t) that makes the functional J as large as possible, while x(t) still satisfies the Vidale-Wolfe IVP and the further restriction that the total market share at time T is fixed at a predetermined level, i.e., x(T ) = x T . In Winkel [5], another author points out how an optimal control problem related to the number of worker and queen bees in a colony can find a place in an ODE course with an emphasis on modeling. Our problem is similar.…”

Section: Optimal Control and Green's Theoremmentioning

confidence: 99%

Find, Process, and Share: An Optimal Control in the Vidale-Wolfe Marketing Model

Barg¹

2018

CODEE

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The Vidale-Wolfe marketing model is a first-order, linear, nonhomogeneous ordinary differential equation (ODE) where the forcing term is proportional to advertising expenditure. With an initial response in sales as the initial condition, the solution of the initial value problem is straightforward for a first undergraduate ODE course. The model serves as an excellent example of many relevant topics for those students whose interests lie in economics, finance, or marketing. Its inclusion in the curriculum is particularly rewarding at an institution without a physics program. The model is not new, but it was novel to us when a group of students chose it for an exploratory project that we designed in order to help students acquire the ability to interpret and communicate mathematical results. In addition to describing the project in this work, we discuss the Vidale-Wolfe model and show how it can lead one to use Green's theorem in a real situation. CODEE Journal

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Section: Optimal Control and Green's Theoremmentioning

confidence: 99%