Solve the Problem $f _ { 1 } ( x ) = - x ^ { 2 } + 100 x ; f _ { 2 } ( x ) = - x ^ { 2 } + 80 x + 200$

question 149

Multiple Choice

Solve the problem.
-The following information pertains to a bakery which makes donuts.


Make a scatterplot of the data. Then graph the following two functions on the same coordinate system: $f _ { 1 } ( x ) = - x ^ { 2 } + 100 x ; f _ { 2 } ( x ) = - x ^ { 2 } + 80 x + 200$ . Decide which function best models the data, and then use that function to estimate the maximum possible profit.

• A) \(\mathrm { f } _ { 1 }\); maximum profit is \(\$ 2500 .\)
• B) \(\mathrm { f } _ { 2 } ;\) maximum profit is \(\$ 1800 .\)
• C) \(\mathrm { f } _ { 1 }\); maximum profit is \(\$ 2900\).
• D) \(\mathrm { f } _ { 2 } ;\) maximum profit is \(\$ 2670 .\)

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Definitions:

Cubic

A common arrangement of atoms in a mineral or the tendency for a mineral to break along three perpendicular planes.

Perpendicular Directions

directions at right angles (90 degrees) to each other.

Nonperpendicular Directions

Directions or orientations that are not at a right angle (90 degrees) to a baseline or reference point.

Explosive Volcanic Eruption

A volcanic eruption characterized by the violent expulsion of magma, gas, and debris from a volcano, often associated with high levels of volcanic ash and pyroclastic flows.