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**11 - 15**of**15**### Appendices

"... Introduction to Solving Linear Programs using LINDO V Table of LINDO commands VI The Simplex Algorithm VII Integer and Integer-Linear Programming: A Branch-and-Bound Algorithm VIII Selected Bibliography Deterministic Optimization and Design Jay R. Lund UC Davis Winter 2000 92 A Derivation of the L ..."

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Introduction to Solving Linear Programs using LINDO V Table of LINDO commands VI The Simplex Algorithm VII Integer and Integer-Linear Programming: A Branch-and-Bound Algorithm VIII Selected Bibliography Deterministic Optimization and Design Jay R. Lund UC Davis Winter 2000 92 A Derivation of the Lagrange Multiplier Method Problem: Max Z = f(X 1 , X 2 ) Subject To (S.T.): g(X 1 , X 2 ) = b, b is a constant If constraint could be reformulated as:X 2 =g 1 X 1 , then the constraint could be substituted into f X 1 ,X 2 and solved as unconstrained optimization. (This is often not possible or expedient. First-order Conditions (2 of 'em) To Max Z, subject to the constraint, a first-order condition is: (1) df dX 1 = 0 = #f #X 1 +<F15.6

### Analyzing Mathematical Programs using MProbe

, 1998

"... Just as modem general-purpose programming languages (e.g. C--, Java) are supported by a suite of tools (debuggers, profilers, etc.), mathematical programming languages need supporting tools. MProbe is an example of a suite of tools supporting a mathematical programming language, in this case AMPL. M ..."

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Just as modem general-purpose programming languages (e.g. C--, Java) are supported by a suite of tools (debuggers, profilers, etc.), mathematical programming languages need supporting tools. MProbe is an example of a suite of tools supporting a mathematical programming language, in this case AMPL. MProbe includes tools for empirically estimating the shape of nonlinear functions of many variables, nonlinearly-constrained region shape, the effect of the objective shape on the ability to find a global optimum, tools for estimating the effectiveness of constraints and for navigating through the model, among others.

### The Simplex Algorithm Integer and Integer-Linear Programming: A Branch-and-Bound Algorithm Selected Bibliography 91 Deterministic Optimization and Design

"... I II III IV V ..."

### ORIGINAL ARTICLE A Mathematical Model of Breast Cancer Treatment with CMF and Doxorubicin

"... Abstract A mathematical model is presented to investigate the ordering phenomenon observed in the comparison of alternating to sequential regimens of CMF (cyclophosphamid, methotrexate, 5-fluorouracil) and doxorubicin used in breast cancer chemo-therapy. The ordinary differential equation model inco ..."

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Abstract A mathematical model is presented to investigate the ordering phenomenon observed in the comparison of alternating to sequential regimens of CMF (cyclophosphamid, methotrexate, 5-fluorouracil) and doxorubicin used in breast cancer chemo-therapy. The ordinary differential equation model incorporates cell cycle specificity and resistance to study why doses of the same drugs given in different orders result in different clinical outcomes. The model employs a pulsing condition to simulate treatment and induced resistance, and we investigate treatment outcome by simulating a patient population by varying parameters using uniform distributions. The results of these simulations correspond to those observed in prior clinical studies and suggest that drug resistance might be a key mechanism in the sequential regimen’s superiority.