Practice Problems - Linear Programming: Modeling and Graphical Solution

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

graph

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?

solution set