Florida B.E.S.T. MA.912.AR.9.8
The Standard
Solve real-world problems involving linear programming in two variables.
Florida B.E.S.T. Standards for Mathematics
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students turn limits from a real situation into linear inequalities in two variables and write an expression to maximize or minimize. They graph the feasible region, test its vertices, and interpret the best result in context.
What Mastery Looks Like
- Students define variables, write the objective and constraints, and graph the shared feasible region accurately. They find every vertex, evaluate the objective at each one, and state the best solution with units and context.
Common Misconceptions
- Students may reverse an inequality, shade the wrong side, or forget that quantities cannot be negative. They may test only one intersection, confuse constraint coefficients with profit values, or round an answer without checking feasibility.
How to Assess It
- Exit ticket: A bakery maximizes 3x + 4y subject to x + 2y ≤ 8, 2x + y ≤ 10, x ≥ 0, and y ≥ 0. Graph the feasible region, list its vertices, and identify the maximum value and where it occurs.
Lesson moves
Ways to Teach It
Overlay colored transparencies for three graphed constraints, mark the shared feasible region, then place counters on each vertex.
Ask students to explain why checking vertices is enough and why a point with greater profit may still be rejected.
Pairs draw two constraint cards and one profit card, graph the region, then race to justify the optimal vertex.
Plan a food truck menu using prep-time and ingredient limits, then choose taco and bowl quantities that maximize profit.
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Related Standards
- MA.912.AR.9.1
Given a mathematical or real-world context, write and solve a system of two-variable linear equations algebraically or graphically.
- MA.912.GR.4.4
Solve mathematical and real-world problems involving the area of two-dimensional figures.
- MA.7.AR.4.5
Solve real-world problems involving proportional relationships.
- MA.912.AR.2.8
Given a mathematical or real-world context, graph the solution set to a two-variable linear inequality.
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