Optimization Problems Quiz

A farmer has 2400 ft. of fencing and wants to fence off a rectangular field that borders a straight river. She needs no fencing along the river. What are the dimensions of the field that has the largest area?

• 600 ft by 1200 ft

• 800 ft by 800 ft

• 1200 ft by 600 ft

• 1000 ft by 1000 ft

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

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

A supermarket employee wants to construct an open-top box from a 14 by 30 cm 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. What size should the squares be in order to create a box with the largest possible volume?

• 3 cm

• 4 cm

• 5 cm

• 6 cm

A rectangular poster is to have 40 square inches of printed area. The top and bottom margins are 2 inches each, and the side margins are 1 inch each. Find the dimensions of the poster such that the least amount of paper is used.

• 6 in by 10 in

• 5 in by 12 in

• 4 in by 11 in

• 7 in by 9 in

A graphic designer is asked to create a movie poster with a 72 cm² photo surrounded by a 2 cm border at the top and bottom and a 1 cm border on each side. What overall dimensions for the poster should the designer choose to use the least amount of paper?

• 10 cm by 12 cm

• 9 cm by 11 cm

• 8 cm by 10 cm

• 7 cm by 9 cm

Find two positive numbers such that the sum of the first plus five times the second is 50 and their product is a maximum.

• 5 and 9

• 10 and 8

• 15 and 7

• 20 and 6

A rancher wants to construct two identical rectangular corrals using 100 m of fencing. The rancher decides to build them adjacent to each other, so they share fencing on one side. What dimensions should the rancher use to construct each corral so that together, they will enclose the largest possible area?

• 10 m by 15 m

• 12.5 m by 12.5 m

• 20 m by 10 m

• 25 m by 5 m

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

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