Optimization (problem Formulation)

You want to make a box to contain dirt and your pet earthworm. Using a 7 in by 10 in rectangle of cardboard, you cut congruent squares from the corners and fold up the sides.

Choose the equation would you use in order to do Calculus to find the maximum volume of dirt (including worm) the box can hold?

• $V=\left(7-2x\right)\left(10-2x\right)$

• $V=x\left(7-2x\right)\left(10-2x\right)$

• $V=x\left(7-x\right)\left(10-x\right)$

• $V=x\left(7+2x\right)\left(10+2x\right)$

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

• -16
• -8
• -4
• 2

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?

•  $F=2x+4y$ 

•  $F=2x+2y$ 

•  $F=xy$ 

•  $F=3\left(x+y\right)$ 

A closed rectangular shipping box with square base is to be made from 120 square inches of cardboard. What dimensions should the box be for maximum volume?

Choose the constraint and optimization equations that represent the problem. 

•  $x^2=120$  and  $V=x^3$  

•  $2x+y=120$  and   $V=xy$  

•  $x^2y=120$  and  $V=2x^2+4xy$  

•  $2x^2+4xy=120$  and  $V=x^2y$  

The volume of a cylindrical tin can with a top and a bottom is to be 16π cubic inches. If a minimum amount of tin is to be used to construct the can, what must be the height, in inches, of the can?

• 2 ³√2
• 2√2
• 4
• 2 ³√4

A closed rectangular shipping box with square base is to be made from 120 square inches of cardboard. What dimensions should the box be for maximum volume?

Choose the constraint and optimization equations that represent the problem. 

•  $x^2=120$  and  $V=x^3$  

•  $2x+y=120$  and   $V=xy$  

•  $x^2y=120$  and  $V=2x^2+4xy$  

•  $2x^2+4xy=120$  and  $V=x^2y$  

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

You want to make a box to contain dirt and your pet earthworm. Using a 7 in by 10 in rectangle of cardboard, you cut congruent squares from the corners and fold up the sides.

Choose the equation you would use in order to do Calculus to find the maximum volume of dirt (including worm) the box can hold?

• $V=\left(7-2x\right)\left(10-2x\right)$

• $V=x\left(7-2x\right)\left(10-2x\right)$

• $V=x\left(7-x\right)\left(10-x\right)$

• $V=x\left(7+2x\right)\left(10+2x\right)$

A closed rectangular shipping box with square base is to be made from 120 square inches of cardboard. What dimensions should the box be for maximum volume?

Choose the  equations that represent the problem. 

•  $x^2=120$  and  $V=x^3$  

•  $2x+y=120$  and   $V=xy$  

•  $x^2y=120$  and  $V=2x^2+4xy$  

•  $2x^2+4xy=120$  and  $V=x^2y$  

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.

• $2x+4y=32$

• $2x+2y=32$

• $xy=32$

• $A=3xy$