iTiaax 3 years ago *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?

1. anonymous

$L + S \le 18$$8\cdot L + 3\cdot S \le 84$

2. iTiaax

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

3. anonymous

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?

4. iTiaax

I understand! Thank you so much!