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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?

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  1. Stiwan
    • 3 years ago
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    \[L + S \le 18\]\[8\cdot L + 3\cdot S \le 84\]

  2. iTiaax
    • 3 years ago
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    Thank you. How do I get to place these inequalities on the graph?

  3. Stiwan
    • 3 years ago
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    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
    • 3 years ago
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    I understand! Thank you so much!

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