Question
PJ owns a small bakery where fresh bread is baked and sold daily. The profit function
p
(
x
)
=
−
3
x
2
+
150
x
models the bakery’s profits, in dollars, as a function of the cost per dozen of mini bread loaves. If PJ wants to earn over $1,800.00 in profits, then what does the price range of the mini bread loaves (per dozen) need to be?(1 point)
Responses
The bread should be priced either less than $4.38 or greater than $45.62 to make a profit of $1,800.00.
The bread should be priced either less than $4.38 or greater than $45.62 to make a profit of $1,800.00.
The bread should be priced either less than $20.00 or greater than $30.00 to make a profit of $1,800.00.
The bread should be priced either less than $20.00 or greater than $30.00 to make a profit of $1,800.00.
The bread should be priced between $20.00 and $30.00 to make a profit of $1,800.00.
The bread should be priced between $20.00 and $30.00 to make a profit of $1,800.00.
The bread should be priced greater than $0.00 and less than $60.00 to make a profit of $1,800.00.
p
(
x
)
=
−
3
x
2
+
150
x
models the bakery’s profits, in dollars, as a function of the cost per dozen of mini bread loaves. If PJ wants to earn over $1,800.00 in profits, then what does the price range of the mini bread loaves (per dozen) need to be?(1 point)
Responses
The bread should be priced either less than $4.38 or greater than $45.62 to make a profit of $1,800.00.
The bread should be priced either less than $4.38 or greater than $45.62 to make a profit of $1,800.00.
The bread should be priced either less than $20.00 or greater than $30.00 to make a profit of $1,800.00.
The bread should be priced either less than $20.00 or greater than $30.00 to make a profit of $1,800.00.
The bread should be priced between $20.00 and $30.00 to make a profit of $1,800.00.
The bread should be priced between $20.00 and $30.00 to make a profit of $1,800.00.
The bread should be priced greater than $0.00 and less than $60.00 to make a profit of $1,800.00.
Answers
GPT-5 mini
Solve −3x^2 + 150x > 1800. Rearranging:
3x^2 − 150x + 1800 < 0 → x^2 − 50x + 600 < 0.
Roots: x = (50 ± √100)/2 = 20 and 30. The quadratic is negative between the roots, so
20 < x < 30.
Thus the bread should be priced between $20.00 and $30.00 per dozen.
3x^2 − 150x + 1800 < 0 → x^2 − 50x + 600 < 0.
Roots: x = (50 ± √100)/2 = 20 and 30. The quadratic is negative between the roots, so
20 < x < 30.
Thus the bread should be priced between $20.00 and $30.00 per dozen.