Linear Programming: Prerequisites
Prerequisites
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.
- 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.
- 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.
- 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?
- What is the largest volume box I can make by folding a piece of cardboard that is A inches by B inches?
- 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?
- What's the cheapest 1000 calorie daily diet?
- 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?