Answer
a) The graph of the system of inequalities is shown below
The wanted regions are the points where the red and blue regions intersect.
We can then see that the suitable points in the wanted region include
(0, 90), (0, 80), (0, 70), (0, 60)
(10, 80), (10, 70), (10, 60)
(20, 70), (20, 60)
(30, 60), (30, 50)
(40, 50)
(50, 40)
(52.5, 37.5)
b) But, we can see that the best solutions are the ones that add up to 90 and use the available resources effectively.
(0, 90), (10, 80), (20, 70), (30, 60), (40, 50), (50, 40), (52.5, 37.5)
So, any of these answers can be picked and will be a possible solution to this system of inequality equations.
Explanation
x represents the number of tacos and y represents the number of burritos.
He can make a maximum of 90 tacos or burritos
x + y ≤ 90
Then, a taco is 3 dollars, and a burrito is 7 dollars.
Jonathan must sell at least 420 dollars worth of tacos and burritos.
3x + 7y ≥ 420
The two inequality equations are
x + y ≤ 90
3x + 7y ≥ 420
We can then plot this graph.
When plotting the graph of linear inequality equations, the first step is to first plot the graph of the straight line normally, using intercepts to generate two points on the linear graph.
If the inequality sign is (< or >), then the line drawn will be a broken line.
If the inequality sign is (≤ or ≥), then the line drawn is an unbroken one.
The shaded region now depends on whether the inequality sign is facing y or not.
It's usually better to write the inequality in terms of y
x + y ≤ 90
3x + 7y ≥ 420
y ≤ -x + 90
y ≥ (-3x/7) + 60
If the inequality sign is facing y, it means numbers above the line plotted are the wanted region and the upper part of the graph is shaded.
If the inequality sign is not facing y, it means numbers below the line plotted are the wanted region and the lower part of the graph is shaded.
The graph of these inequalities are then provided under 'Answer'
Hope this Helps!!!
