The graph of the function C(x) = −0.74x2 + 22x + 75 is shown. The function models the production cost, C, in thousands of dollars for a tech company to manufacture a calculator, where x is the number of calculators produced, in thousands:

graph of a parabola opening down passing through points negative 4 and 57 hundredths comma zero, zero comma 62, 1 and 12 hundredths comma 75, 17 and 65 hundredths comma 167 and 55 hundredths, 34 and 18 hundredths comma 75, and 39 and 87 hundredths comma zero

If the company wants to keep its production costs under $175,000, then which constraint is reasonable for the model?

If the company wants to keep its production costs under $175,000, then 5.6 ≤ x ≤ 24.13 constraint is reasonable for the model given that the function C(x) = −0.74x² + 22x + 75 ,the production cost C, in thousands of dollars for a tech company to manufacture a calculator, where x is the number of calculators produced, in thousands. This can be obtained by using the given graph of the function.

Which constraint is reasonable for the model:

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

From the we have the function,

⇒ C(x) = −0.74x² + 22x + 75

the production cost C, in thousands of dollars for a tech company to manufacture a calculator, x is the number of calculators produced, in thousands.

In the graph the dotted line is the line where C(x) is $175,000. Above this line every the value is greater than $175,000.

The points where this line, that is C(x) = y = 175, intersect the graph of the given function C(x) = −0.74x² + 22x + 75 is (5.6, 175) and (24.13, 175).

This means that above the point (5.6, 175) the graph has the value greater than 175000 and below the point the graph has the value below 175000.

Similarly, below the point (24.13, 175) the graph has the value greater than $175,000 and above the point the graph has the value below $175,000.

Therefore, x ≥ 5.6 and x ≤ 24.13

⇒ 5.6 ≤ x ≤ 24.13

Hence if the company wants to keep its production costs under $175,000, then 5.6 ≤ x ≤ 24.13 constraint is reasonable for the model given that the function C(x) = −0.74x² + 22x + 75 ,the production cost C, in thousands of dollars for a tech company to manufacture a calculator, where x is the number of calculators produced, in thousands.

Learn more about constraints here:

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