Calculus Question

Question

Q.1)In the planning of a coffee shop, we estimate that if there is seating for between 40 and 80 people, the daily profit will be $50 per seat. However, if the seating capacity is more than 80 places, the daily profit per seat will be decreased by $1 for each additional seat over 80. What should the seating capacity be in order to maximize the coffee shop’s total profit?

Q.2)For the question above, what is the profit for the capacity that will maximize the coffee shop's total profit?

Answer 1

P(s) = (50 - s)(80 + s), where s represents each additional seat.

This is a down opening parabola. Transform P(s) into vertex form to determine maximum. This operation is from Algebra 2.