A manufacture determines that the number of drills it can sell is given by the formula D=-3p squared +180p-125, where p is the price of the drills in dollars.
A) At what price will the manufacture sell the maximum number of drills?
B) What is the maximum number of drills that can be sold?
2007-01-16 08:08:02 · 2 answers · asked by nisha10mabry 3 in Science & Mathematics ➔ Mathematics
The maximum will occur at the vertex of the parabola.
A) The answer will be the x-value of the vertex (the first coordinate)
B) The answer will be the y-value of the vertex (the second coordinate)
D = -3p^2 +180p - 125
We can find the vertex by completing the square.
-3p^2 + 180p - 125
= (-3p^2 + 180p) - 125
= -3(p^2 - 60p) - 125
= -3(p^2 - 60p + 900) - 125 - -3(900)
= -3(p-30)^2 - 125 + 1200
= -3(p-30)^2 + 1075
The vertex is (30,1075).
A) The price is $30
B) The maximum number of drills is 1075
2007-01-16 09:03:21 · answer #1 · answered by MsMath 7 · 1⤊ 0⤋
Take the first deviate of the equation and let it equat to zero. Then calculate p.
p = $30
2007-01-16 18:03:07 · answer #2 · answered by Brenmore 5 · 0⤊ 0⤋