## System of Three Equations in Word Problem - from 7.1

The Wittenberger Movie Showings sells two sizes of popcorn, a 1-gallon bucket and a 2-gallon bucket. Due to school policy, they must make at least twice as many 2-gallon buckets as 1-gallon buckets, In addition, the total number of buckets of popcorn made during a single workday cannot exceed 1800 buckets. The company makes $2 profit for each 1-gallon bucket sold, and they make $3 profit for each 2-gallon bucket of popcorn sold. The company would like to maximize their daily profit.

Let x = number of 1-gallon buckets made, y = number of 2-gallon buckets made.

Formulate objective function and constrains.

## Profit Maximization With System of Three Equations - from 7.3

For the previous problem, solve for the maximum profit earned under the given constrains.

## Identify Sets in Graphing - from 7.2

Determine which point lies in the feasible set given by the constrains:

x - y ≥ -1 x - y ≤ 1 x + y > -3 x ≥ 0 y ≥ 0

## Graphing and Corner Point Solutions - from 7.3

Which of the following represents the number of corner points of the solution set to the following system of inequalities? What are their coordinates?

x ≥ -2 y ≥ -3 x + 2y ≤ 10 2x + y ≤ 10

## Unbounded Sets in Graphing - from 7.3

What is the minimum value of the function 8x-3y on the solution set shaded below?