If u me ur will be lucky for the rest of your life

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.

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.

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.

the direct variation says that:

then the equation is of the form is given by:

            where k is the constant variation.

from the given table:

consider any value of x and m(x)=y

x = 2 and m(x)=y = 3

substitute these value in [1]; we have;

divide both sides by 2 we get;

⇒

check:

put x = -1 and m(x) = -1.5

substitute in the equation:

-1.5 = -1.5                   true

therefore, the function m(x) represents a direct variation

graph of this function as shown below:

see attached

step-by-step explanation:

given the function as;

write the equation replacing f(x) with y

form   and fill a table containing values of y with corresponding values of x

you can take a range for   values of x as -3≤x≤3

solving for x=-3

for x=-2

repeat the same procedure to get the values of y for the remaining ,x=-1 to x=3

plot the values of y against values   of x and obtain the following graph