A baseball card store can obtain sports cards at a cost of $5 per card, and has been selling them at a rate of 50 cards per month for a price of$9. The store is planning to change the card price, and estimates that for each $0.50 per card reduction, 10 more cards will be sold each month. At what price per card will the store owner maximize his/her profit? I need to find the answer using calculus and I'm not sure how to solve it using calculus. If you could help me out I would appreciate it. 2. Originally Posted by The Math Man A baseball card store can obtain sports cards at a cost of$5 per card, and has been selling them at a rate of 50 cards per month for a price of $9. The store is planning to change the card price, and estimates that for each$0.50 per card reduction, 10 more cards will be sold each month. At what price per card will the store owner maximize his/her profit? I need to find the answer using calculus and I'm not sure how to solve it using calculus. If you could help me out I would appreciate it.
let x = number of 50 cent reductions

revenue = (number of cards sold)(price per card)

R(x) = (50 + 10x)(9 - .5x)

cost function = (cost per card)(number of cards sold)

C(x) = 5(50 + 10x)

profit = revenue - cost

P(x) = (50 + 10x)(9 - .5x) - 5(50 + 10x) = (50 + 10x)(4 - .5x)

find the maximum profit using the method taught to you in class