Question

*MEDAL WILL BE AWARDED*
A firm uses a combination of large and small boxes to package the items it produces. Large boxes can hold 8 items. Small boxes can hold 3 items. The firm wishes to package 84 or less items using no more than 18 boxes. Let L represent the number of large boxes used and S, the number of small boxes used.

Write down two inequalities, other than L>0 and S>0 to represent the information above.

Also, how do I place these on a graph?

Answer 1

\[L + S \le 18\]\[8\cdot L + 3\cdot S \le 84\]

Answer 2

Thank you. How do I get to place these inequalities on the graph?

Answer 3

I tried to draw the solutions before, but then I think the browser/site crashed. You can look at the two inequalities separately and then take the intersection of their respective solutions. You know \[L + S \le 18 \implies L \le 18 - S,\; S \le 18 - L\] from this follows that L and S take their maximums when the other variable is minimal, in other words when they equal 1, so you know\[1 \le L \le 17, 1 \le S \le 17\] because we only let S and L be positive integers and know S>0, L >0. Everything clear so far?

Answer 4

The graph of inequality 1: http://www.wolframalpha.com/input/?i=1+%3C%3D+L%2C+1+%3C%3D+S%2C+S%2BL+%3C%3D+18
inequality 2: http://www.wolframalpha.com/input/?i=1%3C%3D+S%2C+1%3C%3D+L%2C+8S+%2B+3L+%3C%3D+84
The intersection of both (the area of the solutions):
http://www.wolframalpha.com/input/?i=1%3C%3DS%2C+1%3C%3D+L%2C+L%2BS+%3C%3D+18%2C+8L+%2B+3S+%3C%3D+84

Answer 5

I understand! Thank you so much!