Optimization Practice

same question, now solve it and answer the question:

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

• The overall enclosure should be 8 feet by 8 feet

• The overall enclosure should be 8 feet by 4 feet

• The overall enclosure should be 32 square feet

Tags

CCSS.HSA.CED.A.2

CCSS.HSA.CED.A.3

CCSS.HSA.SSE.A.1

CCSS.HSG.MG.A.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.HSA.CED.A.1

CCSS.HSG.GMD.A.3

CCSS.HSG.MG.A.3

We want to construct a box whose base length is 3 times the base width. If the box must have a volume of 50 ft³, determine the dimensions that will minimize the amount of material used.

• w=2.027ft, h=4.055ft, l=6.082ft
• w=1.488ft, h=3.347ft, l=6.694ft
• w=2.231ft, h=3.347ft, l=6.694ft
• w=0.485ft, h=2.111ft, l=4.222ft

Tags

CCSS.HSA.CED.A.2

CCSS.HSA.CED.A.3

CCSS.HSG.GMD.A.3

CCSS.HSG.MG.A.3

We need to enclose a field with a fence. We have 500 feet of fencing material and a building is on one side of the field so we won't need any fencing on that side. Determine the dimensions of the field that will enclose the largest area. Scan a copy of your work and email it. Only Calculus solutions will be accepted.

• x=250 ft, y=125 ft

• x=150 ft, y=200 ft

• x=125 ft, y=100 ft

• x=200 ft, y=150 ft

Tags

CCSS.HSA.CED.A.2

CCSS.HSA.CED.A.3

A supermarket employee wants to construct an open-top box from a 14 by 30 inch piece of cardboard. To do this, the employee plans to cut out squares of equal size from the four corners so the four sides can be bent upwards to create the box. What size should the squares be in order to create a box with the largest possible volume?

A cryptography expert is deciphering a computer code. To do this, the expert needs to minimize the product of a positive rational number and a negative rational number, given that the positive number is exactly 5 greater than the negative number. What final product is the expert looking for?

• -25

• -20

• -15

• -10

Tags

CCSS.7.EE.B.3

The product of two positive numbers is 200. Find the two numbers if the sum of their squares is to be as small as possible.

• 10 and 20

• 14.14 and 14.14

• 15 and 13.33

• 12.5 and 16