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

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 $\$ 2670 .$