Excel Solver to minimize price while maximizing revenue

tkdlax,

Welcome to the forum!
In your post, you state you are using linear programming. If everything is linear, then we can use some basic algebra to find what you're looking for.

A linear equation is y=m*x+b

To accurately demonstrate model this scenario:
b would be the number of items sold if the product was free
m would be the estimated decline in sales for every 1$ increase in price
x would be the price in 1$ increments
y would be the amount of units sold (the frequency as you called it)

We need to introduce a new variable, r (for revenue). r=y*x (revenue = units sold * price)
So if r=y*x and y=m*x+b then we can substitute y for it's equation counterpart:

r=(m*x+b)*x
r=m*x^2+b*x

Now we can use the peak location of a quadratic to extract the best revenue:
max r = -b/(2*m)