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<h2 class="hd hd-2 unit-title">Slides</h2>
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<h2 class="hd hd-2 unit-title">Graphing Exercise</h2>
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Linear Constraint
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<p>Suppose we have a feasible region, to which we wish to add the additional constraint: \( x+y \leq 2\)</p>
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<p>Which of the graphs below best represents the feasible region after adding the constraint?</p>
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<h2 class="hd hd-2 unit-title">Types of Linear Programs</h2>
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<h2 class="hd hd-2 unit-title">Types of Linear Programs Exercises</h2>
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Linear Programming Solutions
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<p>Which of the following can be true for a Linear Program? (Select all correct answers.)</p>
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There is no feasible solution.
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There is an optimal solution.
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There is a feasible solution but the solution value is unbounded from above.
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There is a feasible solution, and the feasible region is bounded, but there is no optimal solution.
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<h2 class="hd hd-2 unit-title">Convex Sets</h2>
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<h2 class="hd hd-2 unit-title">Convex Sets Exercise</h2>
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Convex Combinations
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<p>In the feasible region below, \(p_1=(0.5,2.0)\) and \(p_2=(3.0,0.5)\). The point (2, 1.1) is on the line segment joining \(p_1 \) and \(p_2 \). Thus (2, 1.1) can be expressed as a "convex combination" of the points \(p_1 \) and \(p_2\). That is, there is a value \(q \) such that \((1-q) \times p_1 + q \times p_2 =(2, 1.1)\). </p>
<p>Find the value of \(q\). Express your answer using decimals rather than fractions. </p>
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<h2 class="hd hd-2 unit-title">Extreme Points Exercise</h2>
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Extreme Points
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<h2 class="hd hd-2 unit-title">Convex Functions</h2>
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<h2 class="hd hd-2 unit-title">Convex Functions Exercise</h2>
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Convex Functions Exercise
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<p>Consider the function \(y = x^a\) where \(0 \lt a \lt 1\) for \(x \in (0, \infty)\). This function is </p>
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Concave
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Convex
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Neither convex nor concave.
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<h2 class="hd hd-2 unit-title">Simplex Method</h2>
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<h2 class="hd hd-2 unit-title">Simplex Method Exercise</h2>
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Simplex Method
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<p>Below is a diagram demonstrating the Simplex Method</p>
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<p>Start at the point \((0,3)\). According to the simplex method, what will the next extreme point be?</p>
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Simplex Step
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<p>Below is a diagram demonstrating the Simplex Method</p>
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<p>Suppose the objective function was [mathjaxinline]6y+3x[/mathjaxinline]. What are the two different paths that the simplex algorithm might take starting at [mathjaxinline](0,0)[/mathjaxinline]?</p>
<p>Choose all that apply</p>
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Simplex Termination
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<p>Suppose that there is no improving direction but there is a direction in which the objective does not change. </p>
<p>Is the current corner point optimal?</p>
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Simplex Termination
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<p>Is there more than one optimal solution?</p>
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