Question

QUESTION 2. the feasible region shows the number of chairs x and tables y that a furniture company can build each week.

part a)can the company build 12 chairs and 5 tables? explain.

part b) can the company build 18 chairs and 3 tables ? explain

part c) one week, te company decides to build 4 tables. how many chairs can the company build?

Answer 1

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

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