Skip to main content
\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)
Mathematics LibreTexts

3.5: Review Problems

  1. Last updated
  2. Save as PDF
  • Page ID
    1842

    • \( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)

    \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)

    1. Maximize \(f(x,y)=2x+3y\) subject to the constraints
    $$
    x\geq0\, ,\quad y\geq0\, ,\quad x+2y\leq2\, ,\quad 2x+y\leq2\, ,
    $$
    by

    a) sketching the region in the \(xy\)-plane defined by the constraints and then checking the values of \(f\) at its corners; and,

    b) the simplex algorithm (\(\textit{Hint:}\) introduce slack variables).

    Contributor