Question

The number of customers in a grocery store is modeled by the function y -X? + 10x + 50, where y is

the number of customers in the store and x is the number of hours after 7:00 A.M.

a. At what time is the maximum number of customers in the store?

- How many customers are in the store at the time in part (a)?

Answer 1

Using the vertex of the quadratic function, it is found that:

a) The maximum number of customers in the store is at 12 P.M.

b) 75 customers are in the store at this time.

The number of customers in x hours after 7 AM is given by:

$y = -x^2 + 10x + 50$

Which is a quadratic equation with coefficients $a = -1, b = 10, c = 50$

Item a:

The maximum value, considering that a < 0, happens at:

$x_v = -\frac{b}{2a}$

Hence:

$x_v = -\frac{10}{2(-1)} = 5$

5 hours after 7 A.M, hence, the maximum number of customers in the store is at 12 P.M.

Item b:

The value is y(5), hence:

$y(5) = -(5)^2 + 10(5) + 50 = 75$

75 customers are in the store at this time.

A similar problem is given at https://brainly.com/question/24713268