# Linear Problem Solving

- [Instructor] Kaylee wants to do well in her classes, so she is budgeting her time carefully to decide the number of classes, C, she will take this year.For each each class that she takes, she expects to spend 2 1/2 hours each week working on homework.So this sentence says it doesn't matter how many classes she takes, she's gonna spend 6 1/2 hours reading.

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Try it risk-free From sale prices to trip distances, many real life problems can be solved using linear equations. Let's say you're a little short on cash and need a loan. You've been averaging way more than that, so maybe this isn't a great plan. If you can save \$35 each week, how many weeks will it take you to get the bike? We focused on defining the variable, or the unknown quantity, in terms of what is known, then solving for the variable.

In this lesson, we'll practice translating word problems into linear equations, then solving the problems. Let's take that knowledge and look at some real life situations. Your cousin agrees to loan you money, and you agree that you'll repay him in full plus 4% interest. But, then you get a new job, and suddenly you have some extra cash. Oh, and we solved the dreaded algebra train problem. You'll be able to translate word problems into linear equations and solve those equations after watching this video lesson. We have over 200 college courses that prepare you to earn credit by exam that is accepted by over 1,500 colleges and universities.

Linear programming is the process of taking various linear inequalities relating to some situation, and finding the "best" value obtainable under those conditions.

A typical example would be taking the limitations of materials and labor, and then determining the "best" production levels for maximal profits under those conditions.

2 1/2 C plus 6 1/2, yup that's what we have over here, is equal to 19, yup that's this choice.

The only difference between this and what I wrote is they just swapped the two sides of the equality which you can always do.She expects to spend an additional 6 1/2 hours each week completing the assigned reading for all of her classes together. She has 19 hours available each week to complete homework and reading for her classes.If Kaylee has 19 hours available each week to complete homework and reading for her classes, which equation best models the situation? So how much time is it going to take her to complete the homework?Well, I like trains, but I still feel a little nervous when I read a math problem that starts with a train. Our variable here is the amount of interest, so let's call that x. Your cell phone company is promoting a text message plan that costs each month plus five cents per text. If I'm going to have to translate a real world scenario to an algebraic equation, can't it be something I might actually encounter in my life? The interest will be the amount of the loan, 0, multiplied by the interest rate, 4%. You currently pay each month for an unlimited plan, but you want to save a few dollars. In "real life", linear programming is part of a very important area of mathematics called "optimization techniques".This field of study (or at least the applied results of it) are used every day in the organization and allocation of resources.So which of these choices are what I just wrote over here?So let's see, they have the 19 on the other side but you see they have 2 1/2 C minus 6 1/2, no that's not this right over here.Then you figure out the coordinates of the corners of this feasibility region (that is, you find the intersection points of the various pairs of lines), and test these corner points in the formula (called the "optimization equation") for which you're trying to find the highest or lowest value.Somebody really smart proved that, for linear systems like this, the maximum and minimum values of the optimization equation will always be on the corners of the feasibility region.