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?
−3.09 ≤ x ≤ 5.6 and 24.13 < x ≤ 32.82
0 ≤ x < 5.6 and 24.13 < x ≤ 32.82
−3.09 ≤ x ≤ 32.82
5.6 ≤ x ≤ 24.13

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shivishivangi1679 shivishivangi1679 · Answer 1 · 2022-04-15T07:54:55+02:00

If the company wants to keep its production costs under $175,000 a reasonable domain for the constraint x is 5.6 ≤ x ≤ 24.13

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

Let x be the number of tires produced, in thousands

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

we have

[tex]C(x) = -0.74x^{2} + 22x + 75[/tex]

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

The vertex represents a maximum

we know that

For the interval (5.6, 24.15] = 5.6 ≤ x ≤ 24.13

The value of C(x) = C(x) < 175

That means the production cost is under $175,000

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

therefore

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

5.6 ≤ x ≤ 24.13

Learn more about constraints;

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elliekoh157 elliekoh157 · Answer 2 · 2022-07-16T18:21:45+02:00

Answer:

A

Step-by-step explanation:

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