Linear Inequalities Concepts
When graphing an inequality, a dashed boundary line is used for these two inequality symbols (answer is how they're read out loud).
What is less than or greater than (< or >)?
These are the limiting conditions placed on an optimization problem and are represented by linear inequalities.
What are constraints?
A sports store has a net revenue of $100 on every pair of downhill skis sold (x) and $120 on every snowboard sold (y). The manager’s goal is to have a net revenue of more than $600 a day from the sales of these two items. The combination of ski and snowboard sales will meet or exceed this daily sales goal is ________
What is 100x + 120 y > 600?
Given the profit function, P = 5x + 3y, the coordinate(s) which maximizes P among: (0,0), (0,4), (6,0) is _______.
What is (0,6)?
In a system of inequalities, this is the part of the graph containing all points that satisfy the inequalities (i.e., the solutions).
What is feasible region?
An optimization problem is one in which a quantity must be ______ or ______, while following a set of constraints
What are maximized or minimized?
Wendy is buying strawberries and blueberries. Strawberries cost $6/pint and blueberries cost $8/pint. Her budget requires her to spend less than $100. If x is # strawberries and y is # blueberries, the inequality representing the cost restriction is ___________?
What is 6x + 8y < 100?
Given the cost function, C = -4x + 6y, the coordinate(s) which maximizes P among: (0,8), (3,5), (10,0) is _______.
What is (10,0)?
Solutions where the variables are restricted to whole numbers look like this.
What is a dotted/stippled region?
This equation represents the relationship between the variables and the quantity being maximized or minimized.
What is the objective function?
A vending machine holds at most 240 cans. At least 2 cans of juice are sold for every can of pop. Juice sells for $1 and pop for $1.25. If x is juice and y is pop, name the two constraints of this linear inequality.
What is x+y ≤ 240 and x ≥ 2y?
A feasible region has vertices (0,0), (0,9), (5,8), (11,0). The revenue function is R = 7x + 4y. What is the maximum revenue (in $)?
What is $77?
The domain and range of x + 4 > 2x and y - 1 < 137
What is x < 4 and y < 138?
In a linear optimization problem with an enclosed feasible region, the maximum or minimum value will occur at the corners/vertices, which lie on the ___________.
What is boundary?
*Systems related*:
An airline has a maximum capacity of 145 passengers. At least 130 economy seats must be sold, and no more than 8 business-class seats can be sold. Business seats (y) generate $615 and economy seats (x) generate $245. The objective (revenue) function representing this problem is __________.
What is R = 245x + 615y?
A business wants to maximize C = 30x + 50y, subject to the constraints x + y ≤ 10; 2x + y ≤ 14; and x≥0, y≥0.
What is (4,6)?