Complete question is;
A model for a company's revenue from selling a software package is R = -2.5p² + 500p, where p is the price in dollars of the software. What price will maximize revenue? Find the maximum revenue.
Answer:
Price to maximize revenue = $100
Maximum revenue = $25000
Step-by-step explanation:
We are told that:
R = -2.5p² + 500p, where p is the price in dollars of the software.
The maximum revenue will occur at the vertex of the parabola.
Thus, the price at this vertex is;
p = -b/2a
Where a = - 2.5 and b = 500
Thus:
p = -500/(2 × -2.5)
p = -500/-5
p = 100 in dollars
Maximum revenue at this price is;
R(100) = -2.5(100)² + 500(100)
R(100) = -25000 + 50000
R(100) = $25000
The length of the shorter piece is 30
<h3>What are algebraic expressions?</h3>
Algebraic expressions are expressions that are made up of constants, terms, factors and variables.
They also contain mathematical operations such as division, addition, multiplication, subtraction, etc
From the information given, we have;
Let the length of one piece be x
Let of the other piece is 5x
5x + x = 180
collect like terms
6x = 180
Make 'x' the subject
x = 180/ 6
x = 30
Thus, the length of the shorter piece is 30
Learn more about algebraic expressions here:
brainly.com/question/4344214
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Step-by-step explanation:
![6x + 3y = 15x = 2and y = 5](https://tex.z-dn.net/?f=6x%20%2B%203y%20%3D%2015x%20%3D%202and%20%20y%20%3D%205%20)
Answer:
A) 21.25 + 0.1m <= 60
B) 387
Step-by-step explanation:
I think the problem means to say that the first 1000 text messages are included in the $21.25 plan, and messages above the included 1000 cost $0.10 each.
A)
Let m = number of text messages above 1000.
0.1m is the cost of the messages past the included 1000.
The cost of the plan ($21.25) plus the cost of the messages above 1000, must cost up to $60.
21.25 + 0.1m <= 60
B)
21.25 + 0.1m <= 60
0.1m <= 38.75
m <= 38.75/0.1
m <= 387.5
Answer: 387