QUESTION 2. the feasible region shows the number of chairs x and tables y that a furniture company can build each week.
1 answer:
Answer:
Part a) The company can not build 12 chairs and 5 tables
Part b) The company can build 18 chairs and 3 tables
Part c) The company can build 12,13,14,15,16 or 17 chairs
Step-by-step explanation:
we know that
If a ordered pair is a solution, then the ordered pair must be belong to the feasible region of the graph
Part a) Can the company build 12 chairs and 5 tables?
In this problem we have the ordered pair A(12,5)
Plot and verify if the point belong to the feasible region of the graph
see the attached figure to better understand the problem
The point A is not on the feasible region
therefore
The company can not build 12 chairs and 5 tables
Part b) Can the company build 18 chairs and 3 tables?
In this problem we have the ordered pair B(18,3)
Plot and verify if the point belong to the feasible region of the graph
see the attached figure to better understand the problem
The point B is on the feasible region
therefore
The company can build 18 chairs and 3 tables
Part c) One week, the company decides to build 4 tables. how many chairs can the company build?
For y=4
Find the value of x in the graph
The solutions point for y=4 tables are
(12,4), (13,4),(14,4),(15,4),(16,4) and (17,4)
therefore
The company can build 12,13,14,15,16 or 17 chairs
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Answer:
Part A) The system of inequalities is
and
Part B) In the procedure
Part C) The schools that Natalie is allowed to attend are A,B and D
Step-by-step explanation:
Part A: Using the graph above, create a system of inequalities that only contain points C and F in the overlapping shaded regions
we have
Points C(2,2), F(3,4)
The system of inequalities could be
-----> inequality A
The solution of the inequality A is the shaded area at the right of the solid line x=2
-----> inequality B
The solution of the inequality B is the shaded area above of the solid line y=2
see the attached figure N 1
Part B: Explain how to verify that the points C and F are solutions to the system of inequalities created in Part A
we know that
If a ordered pair is a solution of the system of inequalities, then the ordered pair must satisfy both inequalities
<em>Verify point C</em>
C(2,2)
<em>Inequality A</em>
----->
----> is true
<em>Inequality B</em>
------>
----> is true
therefore
Point C is a solution of the system of inequalities
<em>Verify point D</em>
F(3,4)
<em>Inequality A</em>
----->
----> is true
<em>Inequality B</em>
------>
----> is true
therefore
Point D is a solution of the system of inequalities
Part C: Natalie can only attend a school in her designated zone. Natalie's zone is defined by y < −2x + 2. Explain how you can identify the schools that Natalie is allowed to attend.
we have
The solution of the inequality is the shaded area below the dotted line
The y-intercept of the dotted line is the point (0,2)
The x-intercept of the dotted line is the point (1,0)
To graph the inequality, plot the intercepts and shade the area below the dotted line
see the attached figure N 2
therefore
The schools that Natalie is allowed to attend are A,B and D
