Sales Analysis—Watercolors: The Colorama Company hires a consulting firm to assess its wor...

Sales Analysis—Watercolors: The Colorama Company hires a consulting firm to assess its work and consequently revises its price and cost functions to

Redo parts (a) to (f) in Exercise 1 using these revisions.

Exercise 1

Sales Analysis—Watercolors: The Colorama Company, a paint manufacturer, has just produced a watercolor set that it sells to wholesalers for $6 each. The cost C(x) to produce x watercolor sets is given by the function

 C(x) = 0.0002x2 + 2x + 1250

(a) Algebraically derive the profit function P(x) and simplify it.

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(b) Evaluate P(3000) and interpret.

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(c) Differentiate to compute the marginal profit function.

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(d) Evaluate MP(3000) and interpret.

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(e) Use the solutions from parts (b) and (d) to get a linear approximation for the value of P(3001).

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(f) Compute the error of the approximation for P(3001) in part (e).