optimization review

Find two real numbers whose difference is 50 and whose product is a minimum.

• 25 and 25

• 40 and -10

• 50 and -50

• 25 and -25

• Cannot be determined

A rectangular piece of land is bordered by a river. The other 3 sides are to be enclosed with 44 feet of fencing.

What is the maximum area that can be enclosed?

• 1936 ft²

• 484 ft²

• 242 ft²

• 121 ft²

• cannot be determined

Find two real numbers whose difference is 50 and whose product is a minimum.

• 25 and 25

• 40 and -10

• 50 and -50

• 25 and -25

• Cannot be determined

Suppose you had 72 m of fencing to make two side-by-side enclosures as shown.

What is the maximum area that you could enclose?

• 216 m²

• 144 m²

• 108 m²

• 2045.5 m²

• cannot be determined

Suppose you had 88 m of fencing to make a three side-by-side enclosures as shown.

What is the maximum area that you could enclose?

• 242 m²

• 121 m²

• 484 m²

• 7744 m²

• cannot be determined

Farmer Jo has 32 square feet of land in which to make an enclosure for bunnies, chicks, and penguins. (see picture)

Choose the equation that represents this information.

same question, but more ...
There will be fencing put in around the entire enclosure and in the middle (as pictured) to create 3 sections, what dimensions should the overall enclosure be in order to use the least amount of fence?

Which equation represents the fence amount (F) that you want to minimize?

A farmer wants to construct a rectangular pigpen using 400 ft of fencing. The pen will be built next to an existing stone wall, so only three sides of fencing need to be constructed to enclose the pen. What dimensions should the farmer use to construct the pen with the largest possible area?

• 100ft x 200ft

• 102ft x 196 ft

• 50 ft x 300 ft

• 50 ft x 175 ft

If y=2x-8, what is the minimum value of the product xy?

• -16
• -8
• -4
• 2