Upper P prime left parenthesis x right parenthesisP?(x) , in cents, is given by

Question

Upper P prime left parenthesis x right parenthesisP?(x) ,

in cents, is given by

Upper P prime left parenthesis x right parenthesis equals negative 0.0007 x cubed plus 0.31 x squared plus 40.6 xP?(x)=?0.0007x3+0.31x2+40.6x

for

x less than or equals 400x?400 ,

where x is the number of members currently enrolled in the club. Approximate the total profit when

240240

members are enrolled by computing the sum

Summation from i equals 1 to 6 Upper P prime left parenthesis x Subscript i Baseline right parenthesis Upper Delta x?i=16P?xi?x

with

Upper Delta x equals 40?x=40.

The total profit when

240240

members are enrolled is approximately

$

Save Score: 0 of 1 pt 5 of 7 (7 complete) Hw Score: 85.71 %, 6 of 7 pts Bus Econ 4.2.19 Question Help * A record club has found that the marginal profit, P (x), in cents, is given by P(x)0000x3+0.31x +40.6x for 24. x s 400, where x is the number of members currently enrolled in the club. Approximate the total profit when 240 -0 90z P'tx,. _ 0.0007x, 0.31x2 + 40b members are enrolled by computing the sum 2P(x) Ax with Ax-40 § 19.200- 14,400 i=1 ,800 111 | IV? VIVI 0 100 200 300 400 Number of members The total profit when 240 members are enrolied is approximately $16,624.00 The total profit when 240 members are enrolled is approximately $ 16,624.00 Round to the nearest cent as needed.)

Explanation / Answer

P(x) = -0.0007x^3+0.31x^2+40.6x

marginal profit = (40) * ( P(0) + P(40) + P(80) + P(120) + P(160) + P(200) )

=(40) * ( 0 + 2075.2 + 4873.6 + 8126.4 + 11564.8 + 14920 )

=1662400 cents

=1662400/100 dollars

=16624.00 dollars

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