A company produces foam mattresses in two​ sizes: regular and king size. It takes 3 minutes to cut the foam for a regular mattress and 5 minutes for a king mattress.

A company produces foam mattresses in two​ sizes: regular and king size. It takes 3 minutes to cut the foam for a regular mattress and 5 minutes for a king mattress. If the cutting department has 25
 ​labor-hours available each​ day, how many regular and king mattresses can be cut in one​ day? Express your answer as a linear inequality with appropriate​ non-negative restrictions and draw its graph.

 Answer

Let x be the number of regular mattresses cut per day and let y be the number of king mattresses cut per day.
Multiply the number of minutes needed by the cutting department to cut the foam for a regular mattress by the number of regular mattresses produced to find the number of minutes spent producing regular mattresses.
The cutting department spends 3x minutes producing regular mattresses.
Multiply the number of minutes needed by the cutting department to cut the foam for a king mattress by the number of king mattresses produced to find the number of minutes spent producing king mattresses.
The cutting department spends 5y minutes producing king mattresses.
The cutting department has no more than 25 labor hours available each day. This is 1500 minutes.
​Thus, the linear inequality with appropriate​ non-negative restrictions is shown below. 

 

The point​ (0,0) satisfies the inequality.

Notice that the number of production minutes cannot be negative so the graph of the solution is restricted to the first quadrant. The graph is shown to the right.

Thanks