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The marginal profit function for seasonal flags produced by the WaveFree Company is given by

MP(x) =

2x

2x2 400

15 x 105

where x is the number of flags produced and sold monthly, and

MP(x)

is the marginal profit in hundreds of dollars.

(a) Determine the marginal profit at a production level of 50 flags produced and sold monthly. (Round your answer to two decimal places.)

When monthly production and sales are 50 flags, the profit from the ---Select--- 49th 50st 51st flag is about $ .

(b) Evaluate

100	MP(x)dx
20

.

100	MP(x)dx
20

= Interpret

100	MP(x)dx
20

.

The total increase in profit of producing and selling from to 100 flags each month is $ .

(c) Knowing that the WaveFree Company breaks even when 20 flags are sold, that is,

P(x) = 0

when

x = 20,

recover the profit function P. (Note that

2x

2x2 400

= 2x(2x² 400)^1/2 P(x) =

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