Linear Programming
A baker has 60 kg of flour and 40 kg of sugar. Cookies and cakes use them in different amounts and earn different profits. How many of each should she bake? Guessing is slow, and trying every plan is endless. Linear programming gives the best plan with a graph and a short list of corner points. In this chapter you draw inequalities, find the region of allowed plans, test its corners, and handle the cases with no best plan or many. Then you turn word problems on factories, diets and deliveries into a plan, and Python checks every answer.
Part of Mathematics · High School (11–12) (chapter 19)
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Linear Inequalities and Feasible Regions
What does the region 3x + 2y at most 12 look like? Draw one inequality, then several together, and shade the points that satisfy them all. Learn to tell a bounded region from an unbounded one, and to find its corner points by solving pairs of boundary lines.
The Corner Point Method
A profit that grows along a straight line must be largest at the edge of what is allowed. Use that idea to find the maximum or minimum of an objective function at the corner points. See why unbounded regions need an extra test, what happens when there is no feasible solution or many, and check each answer with scipy.