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17 February, 04:14

A craftsman can sell 10 jewelry sets for $500 each. He knows that for each additional set he makes, the price of each set will decrease by $25. How many jewelry sets should he make if he wants to maximize his earnings?

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  1. 17 February, 04:30
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    The max warning happens when he makes 15 sets.

    Here is what happens as he makes more and more sets:

    10 sets: $500 each

    Total earned: 10*500=5000

    11 sets: $475 each

    Total earned: 11*475=5225

    12 sets: $450 each

    Total earned: 12*450=5400

    13 sets: $425 each

    Total earned: 13*425=5525

    14 sets: $400 each

    Total earned: 14*400=5600

    15 sets: $375 each

    Total earned: 15*375=5625

    16 sets: $350 each

    Total earned: 16*350=5600

    17 sets: $325 each

    Total earned: 17*325=5525

    18 sets: $300 each

    Total earned: 18*300=5400

    19 sets: $275 each

    Total earned: 19*275=5225

    20 sets: $250 each

    Total earned: 20*250=5000

    21 sets: $225 each

    Total earned: 21*225=4725

    22 sets: $200 each

    Total earned: 22*200=4400

    23 sets: $175 each

    Total earned: 23*175=4025

    24 sets: $150 each

    Total earned: 24*150=3600

    25 sets: $125 each

    Total earned: 25*125=3125

    26 sets: $100 each

    Total earned: 26*100=2600
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