Start with a simple grid.

Take this piece of paper:

Recall the equation for the slope of a line
y = mx + b

An equation with greater/less than sign is an "inequality"

How to graph an inequality.

How to think of "and"

First Steps

Translate the following into inequalities.

  1. I can only I spend as much cash as in my wallet on dinner, dessert, drinks, and a tip and I really want to have dinner and drinks though I might pass on dessert.
  2. You are managing a youth shelter. Kids present with an array of personal challenges, each of which require different levels of attention from your staff. Clients with issue A require 4 hours of attention per week. Issue B, about 2 hours, C requires 16, and D 7. Your budget allows you to staff 75 hours per week.
  3. Breakfast is some eggs, some pancakes, some bacon. You have to have at least twice as many pancakes as eggs. You can't have fewer than 2 strips of bacon.

Graph each of the above inequalities

What is the objective function in each of the following situations?

  1. What is the largest volume box I can make by folding a piece of cardboard that is A inches by B inches?
  2. Pancakes cost $1 each, eggs are 1.50, and blintzes are 2. Pancakes have 200 calories, eggs 125 and blintzes 450. What combination gives me the most calories for 5 dollars?
  3. What's the cheapest 1000 calorie daily diet?
  4. I have information on the level of AOD demand reduction we can expect from public awareness campaigns, DARE visits to public schools, increased treatment slots, and increases in after care. I know the cost of each type program and I have a limited budget. What mix of programs should I institute to have the biggest effect on demand?