A manufacturer has daily costs given by the function C = 20,000 – 220x + 0.045x2

[palmz]

A manufacturer has daily costs given by the function C = 20,000 – 220x + 0.045x2

For each problem, carefully read the question. Create a picture if needed and then work the problem. You must show/explain all work as directed. The answers alone are not sufficient to receive full credit. Once you complete this worksheet save it and turn it in the Drop Box provided.

1. A manufacturer has daily costs given by the function C = 20,000 – 220x + 0.045x2 where C is the cost and x is the number of units produced. How many units should be produced each day to yield the minimum cost for production?

Give a numerical answer, explaining the method you used to find your answers. Also, explain another method which you could have used to find the answer.

2. The height y of a ball (in feet) is given by the function and x is the horizontal distance traveled by the ball.

a) How high is the ball when it leaves the child's hand?
b) How high is the ball at its maximum height?
c) Explain, in words, the method you used in part (b).
d) What is the horizontal distance traveled by the ball when it hits the ground?
e) Explain, in words, what you did to find your answer for part (d).
f) Explain, in words, another method which you could have used to find the answer for part (e).

3. The sum of a number and twice the second number is 24. Determine the two numbers to maximize their product. Show your work (equations, calculations, etc.) If it is easier to describe in detail what you did rather than show something (such as using your calculator), you may do so.

4. A fence is created as shown. The farmer building the fence is using 200 meters of fence. Find the dimensions (the values for x and y) to maximize the area. Show all work (equations, set up and so forth). Again you may describe in words any work that is too difficult to show through typing. For the maximum area, round to the nearest whole number, if needed.

5. The height of a ball above the ground as a function of time is given by the function where h is the height of the ball in feet and t is the time in seconds.

a) When is the ball at a maximum height?
b) What is the maximum height of the ball?
c) When does the ball hit the ground?
d) How high is the ball after 0.3 seconds?
e) When is the ball 2 feet above the ground?
f) Explain the methods you used to find your answers.

6. An indoor track is made up of a rectangular region with two semi-circles at the ends. The distance around the track is to be 400 meters.

a.Draw a figure for this problem. Most of your work will depend on getting an accurate picture. Label the length and width of the rectangular region with x and y.
b. Determine the radius of the semicircular ends of the track in terms of y.
c.Use the result from part b to write and equation in terms of x and y for the distance around the track.
d.Use your result from part c to write the area A of the rectangular section as function of x.
e.What dimensions for the rectangular region maximize the area (of the rectangular region)? Do not attempt to maximize the area for the whole figure
f.Explain in words how you arrived at your answer for part e.

 

[Deleted member 4993]

For each problem, carefully read the question. Create a picture if needed and then work the problem. You must show/explain all work as directed. The answers alone are not sufficient to receive full credit. Once you complete this worksheet save it and turn it in the Drop Box provided.

• A manufacturer has daily costs given by the function C = 20,000 – 220x + 0.045x² where C is the cost and x is the number of units produced. How many units should be produced each day to yield the minimum cost for production?

Answer: Give a numerical answer here (round to the nearest whole number and label):

Explain the method you used to find the answer:

Explain one other method you could have used to find the answer:

• The height y of a ball (in feet) is given by the function and x is the horizontal distance traveled by the ball.

a) How high is the ball when it leaves the child’s hand?

b) How high is the ball at its maximum height?

c) Explain in words the method you used in part b.

d) What is the horizontal distance traveled by the ball when it hits the ground?

e) Explain in words what you did to find your answer for part d.

f) Explain in words another method you could have used to find the answer for part e.

• The sum of a number and twice the second number is 24. Determine the two numbers to maximize their product. Show your work (equations, calculations, etc.) If it is easier to describe in detail what you did rather than show something (such as using your calculator), you may do so.

First Number:

Second Number:

Work:

• A fence is created as shown. The farmer building the fence is using 200 meters of fence. Find the dimensions (the values for x and y) to maximize the area. Show all work (equations, set up and so forth). Again you may describe in words any work that is too difficult to show through typing.

x =

y =

Maximum Area (round to the nearest whole number if needed):

Work:

• The height of a ball above the ground as a function of time is given by the function where h is the height of the ball in feet and t is the time in seconds.

When is the ball at a maximum height? (Round to three decimals if needed).	What is the maximum height of the ball? (Round to the nearest tenth if needed)
When does the ball hit the ground? (Round to the nearest hundredth)	How high is the ball after 0.3 seconds?
When is the ball 2 feet above the ground? (Round to the nearest hundredth if needed).
Explain the methods you used to find your answers.

• An indoor track is made up of a rectangular region with two semi-circles at the ends. The distance around the track is to be 400 meters.

a.Draw a figure for this problem. Most of your work will depend on getting an accurate picture. Label the length and width of the rectangular region with x and y. You do not have to recreate your picture here unless you are easily able to do so.

b. Determine the radius of the semicircular ends of the track in terms of y.

c.Use the result from part b to write and equation in terms of x and y for the distance around the track.

d.Use your result from part c to write the area A of the rectangular section as function of x.

e.What dimensions for the rectangular region maximize the area (of the rectangular region)? Do not attempt to maximize the area for the whole figure!!

f.Explain in words how you arrived at your answer for part e.

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[stapel]

1. A manufacturer has daily costs given by the function C = 20,000 – 220x + 0.045x2 where C is the cost and x is the number of units produced. How many units should be produced each day to yield the minimum cost for production?

Give a numerical answer, explaining the method you used to find your answers. Also, explain another method which you could have used to find the answer.

This is a find-the-vertex-and-interpret exercise. Where are you stuck?

2. The height y of a ball (in feet) is given by the function and x is the horizontal distance traveled by the ball.

When you reply with the missing (graphical?) information, please include a clear listing of all of your efforts so far.

3. The sum of a number and twice the second number is 24. Determine the two numbers to maximize their product.

To learn how to set up and solve "find the number" sorts of exercises, try here[/u][/b].

4. A fence is created as shown....

When you reply with the missing information, please include a clear listing of your efforts so far.

6. An indoor track is made up of a rectangular region with two semi-circles at the ends. The distance around the track is to be 400 meters.

a.Draw a figure for this problem. Most of your work will depend on getting an accurate picture. Label the length and width of the rectangular region with x and y.

What did you draw?