SOLUTION: 4. 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. a. What price will maximize the revenue

Question 930645: 4. 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.
a. What price will maximize the revenue? Give a reason for your answer.
b. What is the maximum revenue? Give a reason for your answer.
Found 2 solutions by TimothyLamb, ewatrrr:
Answer by TimothyLamb(4379) (Show Source): You can put this solution on YOUR website!
R = -2.5p2 + 500p
---
substitute p with x
set R = 0
-2.5xx + 500x = 0
---
the above quadratic equation is in standard form, with a=-2.5, b=500 and c=0
---
to solve the quadratic equation, by using the quadratic formula, copy and paste this:
-2.5 500 0
into this solver: https://sooeet.com/math/quadratic-equation-solver.php
---
the quadratic has a maximum at = ( 100, 25000 )
---
answer:
price for maximum revenue = $100
this is the p (or x) coordinate of the equation's maximum
---
maximum revenue = $25,000
this is the R (or y) coordinate of the equation's maximum
---
Solve and graph linear equations:
https://sooeet.com/math/linear-equation-solver.php
---
Solve quadratic equations, quadratic formula:
https://sooeet.com/math/quadratic-formula-solver.php
---
Solve systems of linear equations up to 6-equations 6-variables:
https://sooeet.com/math/system-of-linear-equations-solver.php
Answer by ewatrrr(24785) (Show Source): You can put this solution on YOUR website!
R = -2.5p2 + 500p
Note: 500/-(-2*2.5) = 100
R = -2.5(p -100)^2 + 25, 000 Parabola opening downward V(100,25,000)
.........
a) p = $100 will maximize the revenue. V(100,25000)max
b) max R = $25,000 . V(100,25000)max

RELATED QUESTIONS
A model for a company's revenue from selling a software package is r = -2.5p (squared)... (answered by stanbon)
A model for a company's revenue is {{{R = -15p^2 + 300p + 12000}}} where p is the price... (answered by nerdybill)
(Revenue) The John Deere company has found that the revenue from sales of heavy-duty... (answered by stanbon)
The car company has found that the revenue from sales of sedans is a function of the unit (answered by Alex.33,ikleyn)
hi, I was going through my math homework and i was wondering if you could help me with... (answered by josgarithmetic)
I have to word problem that I need to have detailed answers for and asap thank you... (answered by mananth)
The senior class at Richmont High School is selling t-shirts to raise money for its prom. (answered by Glaviolette)
The demand equation for a certain product is given by p = 118 −0.045x, where p is the... (answered by Theo)
A manufacturer of microwave ovens believes that the revenue R, in dollars, the company... (answered by ikleyn)