Question 1189250: PERFORMANCE TASK 1 DIRECTION: Julie wants to buy burgers and juice for her and her friends. Each burger costs Php 15 while each cup of juice costs Php 10. She only has Php 70 but needs to buy at least 5 snacks. a. Write a system of linear inequalities to model the given situation. b. Solve the system graphically. c. Find at least 3 possible numbers of burgers and cups of juice that Jane can buy. Justify your answers.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! x = number of burgers.
y = number of cups of juice.
each burgher costs 15 php.
each cup of juice juice costs 10 php.
she only has 70 php in total.
she must buy at least 5 snacks.
her constraint inequalities are:
15x + 10y <= 70
x + y >= 5
x, y >= 0
using the desmos.com calculator, you would graph the opposite of the constraint inequalities.
the area on the graph that is not shaded is your feasible region.
any coordinate point in the unshaded area and any coordinate point on the lines themselves is feasible, as long as the values of those coordinate points are integers.
to ensure that the coordinate point is composed of integers, i graphed x integer values from 0 to 5 and y integers values from 0 to 7.
any point you choose must be on the intersection of the x and y values graphed.
you can see from the graph the coordinate points that are feasible.
i marked 3 of them.
the are (0,7), (1,5) (4,1).
the coordinate points are in (x,y) format.
this means that the first value is the the number of times the value of x is multiplied and the second value is the number of times the value of y is multiplied.
each constraint is evaluated at that point to see if the constraint is satisfied at that point.
for the point (0,7):
x + y >= 5 is satisfied because 0 * 1 + 7 * 1 = 7 which is greater than or equal to 5.
15x + 10y <= 70 is satisfied because 0 * 15 + 7 * 10 = 70 which is smaller than or equal to 70.
for the point (1,5):
x + y >= 5 is satisfied because 1 * 1 + 5 * 1 = 6 which is greater than or equal to 5.
15x + 10y <= 70 is satisfied because 15 * 1 + 10 * 5 = 65 which is smaller than or equal to 70.
for the point (4,1):
x + y is satisfied because 4 * 1 + 1 * 1 = 5 which is greater than or equal to 5.
15x + 10y <= 70 is satisfied because 15 * 4 + 1 * 10 = 70 which is smaller than or equal to 70.
likewise, if you look at all the cross points in the unshaded area of the graph or on the lines themselves, you will find that all the constraints are satisfied.
here's what the graph looks like.
note that, if you created your graph manually, you would not graph the opposite of the inequalities.
in that case, you would graph the equalities and then shade the area on the graph that satisfies the inequalities.
that is much more labor intensive and takes a lot more evaluation to make sure you shade the correct areas.
using the built in capabilities of the desmos.com calculator takes a lot of that away, but, in exchange, you need to know to how to make the desmos.com calculator do what you want it to do and be able to make it shows the reesults in a good fashion.
|
|
|
