The obtained data are analysed as suggested by Miles and Huberman (1994) but at first, time triangulation is done or data's credibility by providing equivalent problem contexts and at different times. (3) To explore the behaviour of problem-solving based on the step of Polya (Rizal, 2011) by way of thinking aloud and in-depth interviews. The second problem (M2), a statement leads to problem-solving. The first problem (M1), the statement does not lead to a resolution. (2) To give two mathematical problems with different characteristics. The attainment of the purpose consisted of several stages: (1) to gain the subject from the mathematic education of first semester students, each of them who has a high, medium, and low competence of mathematic case. So, together we will work through numerous questions where we will have to follow the optimization problem-solving process to find the values that will either maximize or minimize our function.The purpose of this study is to obtain a description of the problem-solving behaviour of mathematics education students. This means that the dimensions of the least costly enclosure are 20 feet long and 30 feet wide. Now all that is left to do is substitute our y-value into our secondary equation to find the x-value. The second derivative is positive at y = 30, so we know that we have a local minimum! Now we will substitute our secondary equation into our primary equation ( the equation we want to minimize) and simplify. What are the two numbers?įirst, we need to find our primary and secondary equations by translating our problem. Suppose we are told that the product of two positive numbers is 192 and the sum is a minimum. Let’s look at a few problems to see how our optimization problem-solving strategies in work.
While this may seem difficult at first, it’s really quite straightforward as we are simply finding two equations, plugging one equation into the other, and then taking the derivative. Step 4: Verify our critical numbers yield the desired optimized result (i.e., maximum or minimum value). Step 3: Take the first derivative of this simplified equation and set it equal to zero to find critical numbers. Step 2: Substitute our secondary equation into our primary equation and simplify. Step 1: Translate the problem using assign symbols, variables, and sketches, when applicable, by finding two equations: one is the primary equation that contains the variable we wish to optimize, and the other is called the secondary equation, which holds the constraints. Solving Optimization Problems (Step-by-Step) It is our job to translate the problem or picture into usable functions to find the extreme values. Optimization is the process of finding maximum and minimum values given constraints using calculus.įor example, you’ll be given a situation where you’re asked to find: Or, on the flip side, have you ever felt like the day couldn’t end fast enough?īoth are trying to optimize the situation! Jenn, Founder Calcworkshop ®, 15+ Years Experience (Licensed & Certified Teacher)