A particular computing company finds that its weekly profit, in dollars, from th

Question

A particular computing company finds that its weekly profit, in dollars, from the production and sale of x laptop computers is P(x) = - 0.003x^3 0.2x^2 + 500x 700. Currently the company builds and sells 10 laptops weekly. What is the current weekly profit? How much profit would be lost if production and sales dropped to 9 laptops weekly? What is the marginal profit when x = 10? Use the answer from part (a)-(c) to estimate the profit resulting from the production and sale of 11 laptops weekly. The current weekly profit is $ (Round to the nearest cent as needed.)

Explanation / Answer

1st we will solve for x=10

a) P(10) = -.003(10)^3-0.2(10)^2+5000-700

= 4277.00   answer

b) now we will solve for x= 9

p(9) = -0.003(9)^3-0.2(9)^2+4500-700

=-2.187 -16.2+4500-700

=3781.61   so they lost   4277-3781.61 = 495,39 answer

c) we will find the derivative 1st

p '(x) =-0.009x^2-0.4x+500

p '(10) =495.1 answer

d) p(11) = -.003(11)^3-0.2(11)^2+5500-700

=4771.81 answer

they gain   494.81 answer

And p '(11) = -0.009(11)^2 -0.4(11) +500

   =-1.089-4.4+500

=494.51 answer

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