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[AP Calculus BC] 5.4a Optimization Problems

Last updated about 2 years ago

6 questions

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Question 1

1.

Square both numbers, add them together, and put the result below
Answer as a decimal rounded to two places

Question 2

2.

(b) One number plus the square root of the other is as large as possible

Once you find the two numbers, enter the results of adding one number plus the square root of the other number below.

Answer as a decimal rounded to two places

Question 3

3.

Write the volume below
Answer as a decimal rounded to two places

Question 4

4.

Add the three numbers (height, width, length) for the dimensions together and write the sum below

Answer as a decimal rounded to two places

Question 5

5.

We are going to fence in a rectangular field. If we look at the field from above the cost of the vertical sides are $10/ft, the cost of the bottom is $2/ft and the cost of the top is $7/ft. If we have $700 determine the dimensions of the field that will maximize the enclosed area.

Find the maximum possible area and write it below

Answer as a decimal rounded to two places

Question 6

6.

We want to build a box whose base length is 6 times the base width and the box will enclose 20 in3. The cost of the material of the sides is $3/in2 and the cost of the top and bottom is $15/in2. Determine the dimensions of the box that will minimize the cost.

Add the length, width, and height together and answer below

Answer as a decimal rounded to ONE place