Problem and Solve English Task

Merapi eruption in 2010 brought disaster last year but also brings fortune, and one of them is sand and stones. sand and stone as cold lava flood will carry over into the river downstream at the time of rain above average for more than three hours. residents of around the river can obtain the fortune of the eruption of Merapi, one of them to become miners river sand in the river-drained by the lava. Then a sand miners in times Gendol expect to be able to sell the sand as much as 1000 m3 every week if he set the price per m3 of Rp 3000, but weekly sales will increase by 100 m3 with any reduction in the price of Rp 100. If x number of units sold per week (x ≥ 1000), look for:
Price function, p (x)
The number of units and the corresponding price that will maximize the weekly revenue
Completion:
x = 1000 + (3.00-p (x)) / 0.1 (100)
= P (x) = 3.00-(0.10) (x-1000) / 100
= 4-0.001x

R (x) = xp (x) = 4x ^ 2-0.001x
dR / dx = 4-0.002x

Critical points is just the end points 1000 and 2000 stationary point, which is obtained by setting dR / dx = 0. The first derivative test (R '(x)> 0 for 1000 ≤ x <2000 and R' (x) <0 for x> 2000) shows that x = 2000 gives the maximum revenue.