Optimization

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  $V=x^2y$  

Tags

CCSS.5.MD.C.5B

CCSS.6.G.A.2

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.

• $2x+4y=32$

• $2x+2y=32$

• $xy=32$

• $A=3xy$

Tags

CCSS.HSA.CED.A.3

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

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.CED.A.2

CCSS.HSA.REI.B.4

CCSS.HSA.SSE.A.1

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

• -16
• -8
• -4
• 2

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.CED.A.2

CCSS.HSA.REI.B.4

CCSS.HSA.SSE.A.1

CCSS.HSA.SSE.B.3

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

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3