SOLUTION: Suppose that the manufacturer of a gas clothes dryer has found​ that, when the unit price is p​ dollars, the revenue R​ (in dollars) is Upper R left parenthesis

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Question 1111304: Suppose that the manufacturer of a gas clothes dryer has found​ that, when the unit price is p​ dollars, the revenue R​ (in dollars) is
Upper R left parenthesis p right parenthesis equals negative 8 p squared plus 48 comma 000 pR(p)=−8p2+48,000p
What unit price should be established for the dryer to maximize​ revenue? What is the maximum​ revenue?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+R%28p%29+=+-8p%5E2+%2B+48000p+
This has the general form:
+y+=+a%2Ax%5E2+%2B+b%2Ax+%2B+c+
( +c=0+ )
The x-value of the vertex ( maximum in this case ) is:
+x%5Bv%5D+=+-b%2F%282a%29+
For your problem:
+p%5Bv%5D+=+-48000%2F%28+2%2A%28-8%29%29+
+p%5Bv%5D+=+3000+
Plug this value back into the eqution
+R%5Bv%5D+=+-8%2A3000%5E2+%2B+48000%2A3000+
+R%5Bv%5D+=+-8%2A9000000+%2B+144000000+
+R%5Bv%5D+=+-72000000+%2B+144000000+
+R%5Bv%5D+=+72000000+
At a unit price of $3,000, the maximum revenue is
$72 million
check my math