In this movie we’ll be looking at a company

that makes checkers and chess sets. And as usual their question will be what strategy

that they need to follow in order to maximize their profit. They have a limit of 1900 boards

available daily and of course the two games use the same kind of playing board. They have

an 80,000 unit limit on how much wood is available daily. We have data on how many pieces of

wood each checkers set requires and how many pieces each chess it requires. There’s a distributor

that sells the sets and the distributor has a limit on how many checkers sets and how

many chess sets they’re willing to take each day. The company knows how profitable the

two games are and so the question as usual is how many sets of each type should they

make in order to maximize their profit and what would that maximum profit be. We’ll let

x represent the number of checkers sets they make daily and y the number of chess sets.

The board constraint if you go back and read the problem carefully is that they have a

limit of 1900 boards available daily, so that means the number of games they make checkers

sets plus chess sets cannot exceed that limit. Their wood constraint is 20 units of wood

for each checkers set, 80 units of wood for each chess set and that total amount of wood

they use cannot exceed their daily supply of wood. The distributor will not handle more

than 1250 checkers sets daily, nor more than 750 chess sets daily. And as usual, we’re

constrained to nonnegative values negative values don’t make sense in this problem or

in most other problems. When we start graphing the constraints we find that the board constraint

gives us the brown line shown here, and if you check to see where the solution region

for the inequality lies it’s the points on or to the left of that brown line. The wood

constraint, when you graph the line 20x + 80y=80,000 you get the red line shown here.

And again the solution region for that second inequality is the half plane that contains

the origin. We have the two distributor constraints the one shown in green x