Question

~~A store owner currently sells an item for $50 and can sell 100 items per week on average. However, market research says that for each $3 decrease in price, the owner will be able to sell 25 more items per week. What price should the owner set so that the weekly maximum profit is realized?

Answer 1

????????????? item ????????????

maebee yu meen him sell a THANG or SUMTHUN

du him mane NE profit wen him sell IT at 50$ ???????????

??????????????????? how much du the THANG kost him ??????????????

????????? will the kost stae the same if him sell more ???????

Answer 2

If the owner reduces the price by 3x dollars, so that each item costs 50-3x dollars, 100+25x items can be sold. The expression we need to look at is (100+25x)(50-3x)=25(4+x)(50-3x)=25(200+38x-3x^2)=5000+950x-75x^2. This expression is maximum when its derivative is zero: 950-150x=0, so x=950/150=19/3=6.33 and 3x=$19. The cost of each item is 50-19=$31, and the owner can sell 100+25x=258.333 items. Well, part of an item can't be sold, so we look at x=6 and 7, item cost=$32 or $29, sales=250 or 275 items, $8000 or $7975. Clearly the owner should sell at $32 per item.