A small shop sells ties each tie for $ 3.50. The daily cost function
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A small shop sells ties each tie for $ 3.50. The daily cost function

[From: ] [author: ] [Date: 12-04-13] [Hit: ]
Find the value of x that will maximize the profit of the store.Thanks!-Each tie sells for $3.50, so if x ties are sold, the revenue (in dollars) is 3.......
is estimated at C (x) dollars, where x is the number of ties sold on a normal day and
c (x) = 0.0006 x ³ - 0.03 x ² +20 x +20. Find the value of x that will maximize the profit of the store.
Tip: L = R - C
Thanks!

-
Each tie sells for $3.50, so if x ties are sold, the revenue (in dollars) is 3.5x

Profit = Revenue - Cost
P(x) = R(x) - C(x)
  = 3.5x - (0.0006 x³ - 0.03 x² + 20x + 20)
  = -0.0006x³ + 0.03x² - 16.5x - 20

dP/dx = -0.0018x² + 0.06x - 16.5

Set dP/dx = 0 and solve for x.

You must have a typo somewhere. dP/dx = 0 has no real solution. Are you sure about the coefficient of x in C(x)? Could it be 2.0? Or is the selling price wrong?
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