a. Answer:
The feasible region is shown in the graph. So we know that the x-axis represents chairs while the y-axis represents tables. The first question asks if the company can build 12 chairs and 5 tables, so we can represent this by the point (12, 5). Taking a look at this point in the graph, we can realize that this is not part of the feasible region. So the conclusion is:
No, the company can't build 12 chairs and 5 tables.
b. Answer:
This second question asks if the company can build 18 chairs and 3 tables, so we can represent this by the point (18, 3). Taking a look at this point in the graph, we can realize that this is point is part of the feasible region. So the conclusion is:
Yes, the company can build 18 chairs and 3 tables.
c. Answer:
In this question we know that the company want to build 4 tables in a week. So this can be represented by the point (x, 4). Therefore, our goal is to find the maximum value of x at which the point lies on the feasible region. By taking a look on the graph, we can realize that this value is x = 17. So:
The company can build 17 chairs.