Question

The production costs, C, in thousands of dollars, for an
energy drink company to manufacture cans of energy
drink is given by the model C(x) = 50 +3.8x -0.0038x^2,
where x is the number of cans of energy drinks produce
in one day, in thousands. The company wants to keep i
production cost at or below $781.12.
Given that x is an element of a subset of the integers,
which of the following constraints satisfy the domain of
C(x)?
The answer choices are in the picture.

Answer 1

If the company wants to keep its production costs under $781.12 a reasonable domain for the constraint x is  -12.9892≤ x ≤ 1012.99.

What are constraints?

A constraint is a condition of an optimization problem that should be satisfied the condition.

Let  x is an element of a subset of the integers,

C(x) is the production cost, in thousands of dollars

$C(x) = 50 +3.8x -0.0038x^2,$

This is a vertical parabola open downward (the leading coefficient is negative)

we know that

For the interval [-12.9892, 1012.99] = -12.9892≤ x ≤ 1012.99

The value of C(x) = C(x) < 781.12

That means the production cost is under $781.12

Remember that the variable x (number of tires) cannot be a negative number.

If the company wants to keep its production costs under $175,000 a reasonable domain for the constraint x is -12.9892≤ x ≤ 1012.99

Learn more about constraints;

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