Question

A monthly magazine is hiring reporters to cover school events and local events. In each magazine, the managing editor wants at least 4 reporters covering local news and at least 1 reporter covering school news. The budget allows for not more than 9 different reporters' articles to be in one magazine. Graph the region that shows the possible combinations of local and school events covered in a magazine.

Short answer

The feasible region contained within the inequalities \(L \geq 4\), \(S \geq 1\), and \(L + S \leq 9\) represents all the possible combinations of local (L) and school events reporters (S) that the monthly magazine can hire, meeting the requirement that at least 4 reporters cover local news events, at least one covers school news events, and not more than 9 reporters' articles are in total.

Step-by-step solution

Formulate the inequalities

The monthly magazine provides constraints: at least 4 reporters covering local news (L), at least one reporter covering school news (S), and not more than 9 reporters in total. These constraints can be modeled with the following inequalities: \\(L \geq 4\) (at least 4 local news reporters), \\(S \geq 1\) (at least one school news reporter), \\(L + S \leq 9\) (not more than 9 reporters in total).

Draw the boundary lines and shade the feasible region

Plot the inequalities produced in Step 1 on a coordinate plane. The feasible region is the area where all conditions (inequalities) are satisfied simultaneously.

Graph the local reporters constraint

To graph \(L \geq 4\), draw a vertical line at \(L = 4\) and shade to the right of the line since it entails values greater than 4.

Graph the school reporters constraint

Next, to graph \(S \geq 1\), draw a horizontal line at \(S = 1\) and shade above this line.

Graph the total reporters constraint

To graph \(L + S \leq 9\), first graph the equation by choosing suitable points such as (0,9) and (9,0), then connect them. Afterwards, shade below the line as this area characterizes fewer reporters (≤ 9).

Identify the feasible region

The feasible region is the area on the graph where all shaded regions intersect. This area denotes the possible combinations of local and school events reporters that meet all conditions in the magazine.