Plant A can produce 6 sedans and 8 minivans per week. Plant B can produce 4 sedans and 5 minivans per week. How many weeks should each plant operate to produce at least 48 ​sedans?

Plant A can produce 6 sedans and 8 minivans per week. Plant B can produce 4 sedans and 5 minivans per week. How many weeks should each plant operate to produce at least 48 ​sedans? Express your answer as a linear inequality with appropriate​ non-negative restrictions and draw its graph. Let x be the number of weeks that plant A is  producing vehicles and let y be the number of weeks that plant B is producing vehicles.

Answer

Multiply the number of sedans produced by plant A per week by the number of weeks that plant A is producing vehicles to find the total number of sedans built in plant A.
The total number of sedans built in plant A is 6x.
Multiply the number of sedans produced by plant B per week by the number of weeks that plant B is producing vehicles to find the total number of sedans built in plant B.
The total number of sedans built in plant B is 4y.

Thus, the linear inequality with appropriate​ non-negative restrictions is shown below.

 

 

The graph consists of a shaded​ half-plane that is either to the right of or to the left of the line. If the line is​ solid, the line is also considered part of the graph.​ Otherwise, it is not.

To determine which​ half-plane to​ shade, select a point that is not on the line as a test point. Substitute the coordinates of the point into the inequality to determine whether the point is a solution.

 

  

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