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?
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
