Question 1089655:
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! the formula is:
y = (x - 10,000 * x) * (20 + 4 * x)
y is the revenue.
x is the number of times that 10,000 is reduced from the price and also the number of times that 4 additional smartphones are sold.
for each reduction of 10,000 in the price of the smartphones, the number of additional smartphones sold is 4.
this is a quadratic equation that is most easily solved by using graphing software.
here's a picture of the graph of y = (120,000 - 10,000 * x) * (20 + 4 * x).
you can see from the graph that the maximum revenue is when x = 3.5.
you would want x to be greater than or equal to 0 since the number of smartphones sold can't be negative.
if you want to know how many smartphones are sold when revenue is equal to 2,400,000, just graph y = 2,400,000 and the intersection of that equation with the quadratic equation will tell you.
you will get y = 2,400,000 when x = 0 or when x = 7
here's a picture of the graph that shows the intersection of the equations of y = (120,000 - 10,000 * x) * (20 + 4 * x) and y = 2,400,000.
when you enter the equations into the graphing software, you remove the commas.
your solution is that revenue will be 2.4 million when x = 0 or when x = 7.
when x = 0, y = (120,000 - 10,000 * x) * (20 + 4 * x) becomes y = (120,000 - 0) * (20 + 0) which results in y = 120,000 * 20 which is equal to 2,400,000.
when x = 7, y = (120,00 - 10,000 * x) * (20 + 4 * x) becomes y = (120,000 - 10,000 * 7) * (20 + 4 * 7) which becomes y = (120,000 - 70,000) * (20 + 28) which results in y = 50,000 * 48 which is equal to 2,400,000.
your solution is that a price of 120,000 or a price of 50,000 will result in total revenue of 2,400,000.
if you did not have graphing software, then you would use the quadratic formula.
before using the quadratic formula, you need to place the equation in standard form of:
0 = ax^2 + bx + c
when it's in this form, you get:
a = coefficient of the x^2 term.
b = coefficient of the x term.
c = the constant term.
your start with y = (120,000 - 10,000 * x) * (20 + 4 * x).
simplify by using the distributive law of multiplication to get:
y = 2,400,000 + 280,000 * x - 200,000 * x - 40,000 * x^2
combine like terms to get:
y = 2,400,000 + 80,000 * x - 40,000 * x^2
since you want your revenue to be 2,400,000, replace y with 2,400,000 to get:
2,400,000 = 2,400,000 + 80,000 * x - 40,000 * x^2
to convert this to standard form, subtract 2,400,000 from both sides of the equation to get:
2,400,000 - 2,400,000 = 2,400,000 - 2,400,000 + 80,000 * x - 40,000 * x^2
combine like terms to get:
0 = 80,000 * x - 40,000 * x^2
rearrange the terms in descending order of degree to get:
0 = -40,000 * x^2 + 80,000 * x
the equation is now in standard form.
a = -40,000
b = 80,000
c = 0
to make the arithmetic simpler, you could divide both sides of this equation by 1000 to get:
0 = -40 * x^2 + 80 * x
a = -40
b = 80
c = 0
since it's still in standard form, you would use the quadratic formula to solve for x.
you will get x = 7 or x = 0.
that's the same solution we got when we looked at the graph of the intersection of the equation of y = (120,000 - 10,000 * x) * (20 + 4 * x) and y = 2,400,000.
the graphing software i used is at https://www.desmos.com/calculator
the quadratic equation solver i used is at https://www.mathsisfun.com/quadratic-equation-solver.html
information about the quadratic formula can be found at http://www.sosmath.com/algebra/quadraticeq/quadraformula/quadraformula.html
i'll be available to answer any questions you might have regarding this.
|
|
|
