Question 1110688
the equation is y = -16 * (x-30)^2 + 10,000


simplify to get y = -16 * (x^2 - 60x + 900) + 10,000


simplify further to get y = -16x^2 + 960x - 14,400 + 10,000


combine like terms to get y = -16x^2 + 960x - 4,400


set y = 0 to get -16x^2 + 960x - 4,400 = 0


since this is in standard quadratic form, then:


a = coefficient of x^2 term = -16
b = coefficient of x term = 960
c = constant term = -4,400


the maximum value is when x = -b/2a.


solve for x to get x = -960 / -32 = 30


when x = 30, the original equation becomes y = -16 * (30-30) + 10,000


solve for y to get y = 10,000


looks like the maximum number of shirts to be sold is 10,000 when the price per shirt is equal to 30.


here's the graph of the original equation.


<img src = "http://theo.x10hosting.com/2018/022803.jpg" alt="$$$" >


the maximum revenue will be 10,000 * 30 = 300,000.


the x intercepts for the function will be when the value of y is equal to 0.


the original equation becomes -16(x-30)^2 + 10,000 = 0


subtract 10,000 from both sides to get -16(x-30)^2 = -10,000


divide both sides by -16 to get (x-30)^2 = -10,000 / -16


take the square root of both sides to get x-30 = plus or minus sqrt(10,000/16)


simplify to get x = 30 = plus or minus 25.


solve for x to get x = 5 or 55.


y = 0 when x = 5 or when x = 55.


the graph shows that as well.