SOLUTION: The daily profit P (in thousands of dollars) from the sale of textbooks is a function of the number x of the textbooks sold( in Hundreds. The formula for this function is:
P=-5
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-> SOLUTION: The daily profit P (in thousands of dollars) from the sale of textbooks is a function of the number x of the textbooks sold( in Hundreds. The formula for this function is:
P=-5
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Question 753836: The daily profit P (in thousands of dollars) from the sale of textbooks is a function of the number x of the textbooks sold( in Hundreds. The formula for this function is:
P=-5x^2+11x-4
What sales amount results in the maximum daily profit? what is the maximum daily profit?
Sales amount=" ??? " textbooks
(Round off your answer to a whole number.)
Maximum daily profit= "?????" dollars
(Round off your answer to a whole number.)
You can put this solution on YOUR website! The given equation is P=-5x^2+11x-4. We can use calculus or solve by algebra let me show you both method.
Calculus method
We know that maximum or minimum value occur at critical points hence we find derivative of P and set them equal to 0 to find critical points.
P' = -10x + 11
-10x+11=0
x=11/10
x=1.1
The sale amount is 1.1*100=110.
The daily profit is
P=-5(1.1)^2+11(1.1)-4
p=2.05 Thousand dollars
p=$2050.
Algebra Method:
We know that maximum or minimum value occurs at vertex hence we find vertex of given equation.
x=-b/2a
x=-11/-10
x=1.1*100
x=110
Next we plug x in p to find daily profit.
P=-5(1.1)^2+11(1.1)-4
p=2.05 Thousands
p=2050
