Maximize Area

In other words...what are the vertices of the feasible region?

• (0, 0), (0, 6), (6, 2), (8, 0)

• (0, 0), (6, 0), (2, 6), (0, 8)

When graphing constraints, what do you call the area where all the shading overlaps?

• the answer

• the feasible region

• the void

• the objective function

Identify the profit maximizing level of output for this monopoly firm.

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It is a method for finding a maximum or minimum value of some quantity, given a set of constraints.

• Operations research

• Maximization

• Minimization

• Linear programming

• y = 2.5

  x = 4.5

• y = 16/3π

  x = 2π

• y = 4 + 16/π

  x = 8 + 32/π

• y = 16π - 28

  x = 24π/7

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

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.

• x=250 ft, y=125 ft

• x=150 ft, y=200 ft

• x=125 ft, y=100 ft

• x=200 ft, y=150 ft

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

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?

• 14.67 ft by 73.33 ft

• 11 ft by 44 ft

• 11 ft by 11 ft

• 22 ft by 22 ft

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