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Math help ASAP!!!!!!!!!!?
A baseball card store can obtain Hank Aaron cards at a cost of $5 per card. the store has been selling the cards at $10 each and at this price, has been selling 25 cards per month. The store is planning to lower the price and estimates that for each 25 cent reduction in the price, 5 more cards will be sold each month. At what price should the cards be sold to maximize total monthly profit?
1 Answer
- Simon van DijkLv 68 years agoFavorite Answer
It sells now 25 cards per month giving a profit of $ 50.
If the price is reduced x times 25 ct it sells 5.x more cards
In this way they sell 25 + 5.x cards for a profit of $ 10.00 - $ 5.00 - x. $ 0.25 each
The total profit would be (25 + 5.x).($ 5.00 - x.$0.25) = 125 - x.6.25 + 25.x - 1.25.x^2 = 125 + 18.75.x - 1.25.x^2 This is a parabola with a maximum at (diferentiate) 18.75 - 2.5.x = 0
so at x = 7.5. The price should be $ 10.00 - 7.5 . $ 0.25 = $ 8.14
