SOLUTION: A manufacturer of microwave ovens believes that the revenue R, in dollars, that the company receives is related to the price P, in dollars, of an oven by the function R(P) = 110P –

Algebra ->  Equations -> SOLUTION: A manufacturer of microwave ovens believes that the revenue R, in dollars, that the company receives is related to the price P, in dollars, of an oven by the function R(P) = 110P –      Log On


   



Question 1059344: A manufacturer of microwave ovens believes that the revenue R, in dollars, that the company receives is related to the price P, in dollars, of an oven by the function R(P) = 110P – 0.25P^2. What price will give the maximum revenue?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+R%28P%29+=+110P+-+.25P%5E2+
Use the formula for the vertex
of a parabola, +P%5Bv%5D+=+-b%2F%282a%29+
+a+=+-.25+
+b+=+110+
+P%5Bv%5D+=+-110%2F%28+2%2A%28-.25%29%29+
+P%5Bv%5D+=+110%2F.5+
+P%5Bv%5D+=+220+
$220 gives the maximum revenue
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check:
+R%28220%29+=+110%2A220+-+.25%2A220%5E2+
+R%28220%29+=++24200+-+12100+
+R%28220%29+=+12100+
The maximum revenue is $12,100
Here's the plot:
+graph%28+500%2C+500%2C+-100%2C+500%2C+-1500%2C+15000%2C+-.25x%5E2+%2B+110x+%29+
Looks about right