HW Optimization

A carpenter is building a rectangular room with a fixed perimeter of 100 feet. What are the dimensions of the largest room that can be built? What is its area? #1

• 10 ft by 90ft; 900 ft^2

• 25 ft by 25 ft; 625 ft^2

• 50 ft by 50 ft; 2500 ft^2

• 25 ft by 75 ft; 1875 ft^2

Tags

CCSS.HSA.CED.A.2

CCSS.HSA.CED.A.3

CCSS.HSA.REI.B.4

CCSS.HSA.SSE.A.1

CCSS.HSG.MG.A.3

A carpenter is building a rectangular room with a fixed perimeter of 400 feet. What are the dimensions of the largest room that can be built? What is its area? #2

• 100 ft by 100 ft; 10,000 ft^2

• 100 ft by 300 ft; 30,000 ft^2

• 200 ft by 200 ft; 40,000 ft^2

• 40 ft by 360ft; 14,400 ft^2

Tags

CCSS.HSA.CED.A.2

CCSS.HSA.CED.A.3

CCSS.HSG.MG.A.3

From a thin piece of cardboard 30 inches by 30 inches, square corners are cut out so that the sides can be folded up to make a box. What dimensions will yield a box of maximum volume? What is the maximum volume? Round to the nearest tenth, if necessary. #3

• 10 in. by 10 in. by 10 in.; 1000 in.^3

• 20 in. by 20 in. by 10 in.; 4000 in.^3

• 20 in. by 20 in. by 5 in.; 2000 in.^3

• 15 in. by 15 in. by 7.5 in.; 1687.5 in.^3

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.CED.A.2

CCSS.HSA.REI.B.4

CCSS.HSG.GMD.A.3

From a thin piece of cardboard 10 inches by 10 inches, square corners are cut out so that the sides can be folded up to make a box. What dimensions will yield a box of maximum volume? What is the maximum volume? Round to the nearest tenth, if necessary. #4

• 6.7 in. by 6.7 in. by 3.3 in.; 148.1 in.^3

• 3.3 in. by 3.3 in. by 3.3 in.; 37 in.^3

• 5 in. by 5 in. by 2.5 in.; 62.5 in.^3

• 6.7 in. by 6.7 in. by 1.7 in.; 74.1 in.^3

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.REI.B.4

CCSS.HSG.GMD.A.3

A farmer decides to make three identical pens with 88 feet of fence. The pens will be next to each other sharing a fence and will be up against a barn. The barn side needs no fence. What dimensions for the total enclosure (rectangle including all pens) will make the area as large as possible? #5

• 14.67 ft by 73.33 ft

• 11 ft by 44 ft

• 11 ft by 11 ft

• 22 ft by 22 ft

Tags

CCSS.HSA.CED.A.2

CCSS.HSA.CED.A.3

CCSS.HSA.REI.B.4

CCSS.HSA.SSE.A.1

A farmer decides to make three identical pens with 136 feet of fence. The pens will be next to each other sharing a fence and will be up against a barn. The barn side needs no fence. What dimensions for the total enclosure (rectangle including all pens) will make the area as large as possible? #6

• 34 ft by 34 ft

• 17 ft by 17 ft

• 22.67 ft by 113.33 ft

• 17 ft by 68 ft

Tags

CCSS.HSA.CED.A.2

CCSS.HSA.CED.A.3

Find the number of units that must be produced and sold to yield the maximum profit, given the following equations for revenue and cost: R(x) = 50x - 0.5x² C(x) = 4x + 3. #7

• 47 units

• 49 units

• 54 units

• 46 units

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.REI.B.4

CCSS.HSA.SSE.A.1

Find the number of units that must be produced and sold to yield the maximum profit, given the following equations for revenue and cost: R(x) = 5x C(x) = 0.001x^2 + 1.3x + 30. #8

• 3700 units

• 3150 units

• 1850 units

• 6300 units

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.REI.B.4

CCSS.HSA.SSE.A.1

If the price charged for a bolt is p cents, then x thousand bolts will be sold in a certain hardware store, where p = 130 - x/24. How many bolts must be sold to maximize revenue? #9

• 1560 bolts

• 3120 thousand bolts

• 1560 thousand bolts

• 3120 bolts

Tags

CCSS.HSA.CED.A.2

CCSS.HSA.REI.B.4

CCSS.HSA.SSE.A.1

The price P of a certain computer system decreases immediately after its introduction and then increases. If the price P is estimated by the formula P = 170t² - 1700t + 6400, where t is the time in months from its introduction, find the time until the minimum price is reached. #10

• 5 months

• 10 months

• 20 months

• 8.5 months

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.REI.B.4

CCSS.HSA.SSE.A.1