(please explain with brief explinationa)

a distributor of apple juice has 5000 bottle in the store that it wishes to distribute in a month. from experience it is known that demand D (in number of bottles) is given by D = -2000p² + 2000p + 1700. the price per bottle that will result zero inventory is

To find the price per bottle that will result in zero inventory, we need to find the price (p) at which the demand (D) equals zero.

Given the demand function D = -2000p² + 2000p + 1700, we can set D equal to zero and solve for p.

-2000p² + 2000p + 1700 = 0

To solve this quadratic equation, we can use the quadratic formula:

p = (-b ± √(b² - 4ac)) / (2a)

Comparing the equation to the standard quadratic form ax² + bx + c = 0, we have:
a = -2000
b = 2000
c = 1700

Substituting the values into the quadratic formula:

p = (-(2000) ± √((2000)² - 4(-2000)(1700))) / (2(-2000))

Simplifying the equation further will give us the two possible values of p.

p = (-2000 ± √(4000000 + 13600000)) / (-4000)

Calculating the square root and simplifying further:

p = (-2000 ± √(17600000)) / (-4000)

p = (-2000 ± 4200) / (-4000)

This gives us two possible values for p:

p₁ = (-2000 + 4200) / (-4000)
p₁ = 2200 / (-4000)
p₁ = -0.55

p₂ = (-2000 - 4200) / (-4000)
p₂ = -6200 / (-4000)
p₂ = 1.55

So, the price per bottle that will result in zero inventory is either -0.55 or 1.55. However, it's important to note that negative prices are not realistic in this context, so we can consider the price to be 1.55.