tal-revenue and total-cost functions, find the total profit, the maximum value of the total profit, and the value of x at which it occurs.
Upper R left parenthesis x right parenthesis equals 1300 x minus x squared, Upper C left parenthesis x right parenthesis equals 3000 plus 30 x
The total profit, P(x)equals
negative x squared plus 1270 x minus 3000.
(Simplify your answer. Do not factor.)
Here is their argument. Given the obtuse angle x, we make a quadrilateral ABCD
with ∠DAB = x, and ∠ABC = 90◦
, and AD = BC. Say the perpendicular bisector
to DC meets the perpendicular bisector to AB at P. Then P A = P B and P C =
P D. So the triangles P AD and P BC have equal sides and are congruent. Thus
∠P AD = ∠P BC. But P AB is isosceles, hence ∠P AB = ∠P BA. Subtracting, gives
x = ∠P AD − ∠P AB = ∠P BC − ∠P BA = 90◦
. This is a preposterous conclusion –
just where is the mistake in the “proof” and why does the argument break down there?