Lesson 5: 4.7 Optimization Problems
Duration of Days: 4
Lesson Objective
To determine the maximum or minimum parameters of one set of variables while conforming to a given set of constraints.
- How can we optimize a variable quantity?
- What quantity are we trying to optimize?
- Are we trying to maximize that quantity or minimize it?
- What are the constraints or restrictions?
- What equations from geometry and/or algebra are relevant?
- How can derivatives help with optimization?
- optimization (maximizing/minimizing)
(Application of derivatives in order to optimize a function.)
- Use given parameters and constraints to optimize a related function.
- DOK levels 1-4
- demand, revenue, profit, marginal profit functions
- minimizing amount of material used to create a container with fixed volume
- utilizing a fixed amount of fence to create the largest possible area
Students may have difficulty determining which geometric formulas to use and will likely require review of many basic area, volume, surface area formulas.
Homogeneous grouping and whole class discussion
section assessment
problems assigned from book