Help please try showing your work! ty 1. The sum of two numbers is 16. Find the numbers if the sum of their squares is a minimum.

2. Find 2 numbers whose sum is 120 and whose product is a maximum.

3. Jasmine makes necklace for her market stall. Her daily profit from making necklaces is given by P(x) = -x2 + 20x
dollars.
a. How many necklaces should she make per day to maximize her profit?
b. Find the maximum daily profit that Jasmine can make.

4. The perimeter of a rectangle is 400m. What are the dimensions if the area is a maximum?

5. A rectangular field beside a river is to be fenced on 3 sides. Find the dimensions that produce the maximum area,
if $180 can be spent and the fencing costs$2.25/m.
I

6. A theater seats 4,000 people and charges $20/ticket. At this price, all the tickets are sold. A survey indicates that
if the ticket price is increased, the number of tickets sold will decrease by 200 for every $2 increase. Wat ticket
price will result in the greatest revenue?