What are 3 different ways of solving a system of linear equations?
Provide the names of each method.
Describe each method.
How are systems of linear equations related to minimization and maximization?
Given the following linear programming problem, maximize the solution and then explain how you arrived at your answer.
Include the following:
Graph
Corner points
Checked solution
A concession stand makes $1 on each hot dog and $1.50 on each hamburger. On a typical Saturday, the stand sells between 25
and 40 hot dogs and between 30 and 50 hamburgers. The total sales have never exceeded 80 items (hot dogs + hamburgers).
How many hot dogs and how many hamburgers should be prepared to maximize profit?
Variables
x = Number of hot dogs
y = Number of hamburgers
Constraints
20 < x < 40
30 < y < 50
x + y < 80
Function to Maximize Profit
P = 1x + 1.5y
Graph the constraints on the same grid. There will be two vertical lines (at x = 20 and at x = 40), there will be two
horizontal lines (at y = 30 and y = 50), and a diagonal line (with a y-intercept at 80 and an x-intercept at 80). The
overlapping shaded regions will form a trapezoid with 4 corner points (vertices). Three of the corner points are (20, 30),
(40, 30), and (20, 50). What is the last corner point where the lines x + y = 80 and y = 50 intersect?
Plug all 4 corner points into the objective function to maximize profit.
What is your largest profit? How many hot dogs and how many hamburgers should be prepared to maximize profit?
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