Optimization 1

The population (in thousands) of a certain kind of insect after t months is given by the following formula.

P(t) = 3t + sin(4t) + 100

What is the maximum population and the value of t in monts, within the first 4 months.

• 111,900 at t=3.7463

• 111 at t=3.7463

• 11,900 at t=2.2

• 211,900 at t=3.7463

How do we find the maximum volume of the box given on the left?

• Express the volume as a function of a single variable.

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What is the primary goal when solving the rectangle optimization problem discussed in the first section?

• Minimize the area

• Maximize the perimeter

• Minimize the perimeter

• Maximize the area

What is the primary mathematical method used to find the dimensions that minimize or maximize the function in these optimization problems?

• Algebraic manipulation

• Differentiation

• Geometric analysis

• Integration

In the farmer's fencing problem, what is the main objective for the dimensions of the field?

• Minimize the area of the field

• Maximize the area of the field

• Minimize the cost of fencing

• Maximize the length of the fence

In the context of the cylinder inscribed in a sphere, what is the goal of the optimization problem?

• Minimize the height of the cylinder

• Maximize the volume of the cylinder

• Maximize the radius of the cylinder

• Minimize the volume of the cylinder

For the box with a square base, what aspect is being minimized according to the problem statement?

• The volume of the box

• The base area of the box

• The surface area of the box

• The height of the box