## Related questions with answers

Question

Use graphical methods to solve each linear programming problem.

$\begin{array}{lr} \text{Minimize} & z=x+3 y \\ \text{subject to:} & x+y \leq 10 \\ & 5 x+2 y \geq 20 \\ & -x+2 y \geq 0 \\ & x \geq 0 \\ & y \geq 0. \end{array}$

Solution

VerifiedStep 1

1 of 3${\bf 1. Sketch the feasible region by following the steps:}$

1.1 Draw the corresponding lines (strict inequality: dashed, nonstrict: solid)

1.2 Use test points (usually (0,0), if not on the line) to decide which region to shade

${\bf 2. Find corner points}$ either

2.1 graphically, or

2.2 solve systems of 2 line equations

${\bf 3. Set up a table for corner points, calculate objective function values}$

${\bf 4. Find minimum}$/${\bf maximum}$

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