Question

Photo Necessities produces camera cases. They have found that the cost, c(x), of making x camera cases is a quadratic function in terms of x. The company also discovered that it costs $52 to produce 3 camera cases, $232 to produce 7 camera cases, and $637 to produce 12 camera cases.

A) Write the quadratic function c(x) that models the cost of making x camera cases.

B) Determine the cost of making 5 camera cases.

Answer 1

The quadratic function that models the cost of making x camera cases is c(x) = 10x^2 - 27x + 52. The cost of making 5 camera cases is $167.

Step-by-step explanation:

A) To find the quadratic function that models the cost of making x camera cases, we need to use the given information. We know that it costs $52 to produce 3 cases, $232 to produce 7 cases, and $637 to produce 12 cases. We can set up three equations using these values:

c(3) = 52

c(7) = 232

c(12) = 637

By substituting the values into the quadratic function c(x) = ax^2 + bx + c, we can solve for a, b, and c.

Solving the system of equations, we find that the quadratic function c(x) = 10x^2 - 27x + 52 models the cost of making x camera cases.

B) To determine the cost of making 5 camera cases, we substitute x = 5 into the quadratic function c(x) and solve:

c(5) = 10(5)^2 - 27(5) + 52

c(5) = 250 - 135 + 52

c(5) = 167

Therefore, the cost of making 5 camera cases is $167.