You can put this solution on YOUR website!
don't know if this is the answer you are looking for, but here is an answer.
the trick to making an equation that can be graphed in x and y coordinates is to create an equation that makes y a function of x.
before we do that, we create an equation expressing the relationship we are looking for.
first i will plot revenue as a function of price and units sold.
then i will plot number of units sold as a function of price.
you may want to reverse that, i.e. plot number of unit sold as a function of price, then plot revenue as a function of price and units sold.
i believe they are looking only for the equation of number of units sold in relationship to price.
if that's all you're interested in, skip to the second equation.
otherwise, read read on.
revenue per month = units sold per month * price per unit
let R = revenue per month
let U = number of units sold per month
let P = price
then R = P * U
let 1*x = x = increase in price
let 3*x = decrease in number of units sold
formula for determining Revenue when price increases by $1.00 is then given by the equation
R = (P + x) * (U - 3*x)
this makes revenue a function of price and number of units sold
if we know that P in the equation is a constant of 40, we can substitute 40 for P.
if we know that U in the equation is a constant 60, we can substitute 60 for U.
equation then becomes
R = (x+40) * (60 - 3*x)
in order to graph this equation, i will let y = R.
plotting some points yield the following:
when x = 0, revenue = 40 * 60 = 2400
when x = 1, revenue = 41 * 57 = 2337
when x = 2, revenue = 42 * 54 = 2268
creating a graph, i took x values from -30 to +30.
i had to do this so that the x values and the y values would cross the x and y axis, otherwise the graph wouldn't appear correctly.
i took y values from -21 to 30
the y values plot revenue in hundreds of dollars. this was necessary to keep the y values within a reasonable range in relationship to the x values, otherwise the graph wouldn't come out correctly.
for example, a plot of 24 on the y axis means a revenue of 2400 dollars.
please note that while the increase in price is linear and the drop in number of units sold is linear, the change in revenue is not linear, i.e. it does not follow a straight line. in fact, it looks more like a parabola with a maximum y value around x = -10 or so.
below the graph for revenue i will plot the graph for number of units sold as a function of price, so keep scanning down until you get to the end. that graph will be linear.
revenue graph looks like the following:
plotting number of units sold as a function of price is done in a similar fashion, i.e. the y value is number of units sold and the x value is used to represent the change in price.
the equation we are looking for is y = 60 - 3*x
this graph will be linear.
when x increases by 1, y decreases by 3 which satisfies the requirements.
the number of units sold graph looks like the following:
this graph shows that as price increases by 1, units sold decreases by 3.
for x = -30, y = 60 -(-90) = 60+90 = 150
fox x = -15, y = 60 - (-45) = 60 + 45 = 105
for x = 0, y = 60
for x = 15, y = 60 - 45 = 15
for x = 30, y = 60 - 90 = -30