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Profit Function and Maximum Profit

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A manufacturer finds that the total profit from producing and selling Q units of a product is given by the profit function:

Total Profit = f(Q) = - 460 + 100Q - Q^2

1. Compute the value of the function at Q=10

Total Profit = f(10)= - 460 + 100(10) - 10^2
Total Profit = f(10)= - 460 + 1000 - 100
Total Profit = f(10)=540 - 100
Total Profit = f(10)=440

2. Compute the value of the first derivative of the function at Q=10

3. Explain the significance of each computation.

4. At what level of Q is Profit equal to 1,815?

5. Use Calculus: At what level of Q will Total Profit be a maximum?

6. Double-check your answer to part 5 with an Excel graph.

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A manufacturer finds that the total profit from producing and selling Q units of a product is given by the profit function:

Total Profit = f(Q) = - 460 + 100Q - Q^2

1. Compute the value of the function at Q=10

Total Profit = f(10) = - 460 + 100(10) - 10^2
Total Profit = f(10) = - 460 + 1000 - 100
Total Profit = f(10) = 540 - 100
Total Profit = f(10) = 440

2. Compute the value of the first derivative of the ...

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Sandhya Sharma, MSc
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  • BSc, Meerut University
  • MSc, Meerut University
  • MPhil, Institute of Advanced Studies
  • MSc, AIT
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