You are responsible for maintenance for a fleet of delivery trucks. Truck number 1517 traveled 551.7 miles and used 23.6 gallons
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To find the vertex of our parabola, we are going to use the vertex formula: For a quadratic of the form 
it vertex 
is given by 
, 
.
We can infet from our parabola that
and 
. So lets replace those values in our formula:
The vertex of our parabola is 
Now to find our second point, we are going to evaluate our parabola at
Our second point is
We can conclude that we can graph the parabola
using its vertex and the point as follows:
We can infet from our parabola that
The vertex
Now to find our second point, we are going to evaluate our parabola at
Our second point is
We can conclude that we can graph the parabola
Q(p) = k/p^3 . . . . . . . . we want to find k
q(10) = k/10^3 = 64
k = 64,000
Revenue = q(p)*p = 64000/p^2
Cost = 150 +2q = 150 +2*64000/p^3
Profit = Revenue -Cost = 64000/p^2(1 -2/p) -150
Differentiating to find the maximum profit, we have
.. dProfit/dp = -2(64000/p^3) +6(64000/p^4) = 0
.. -1 +3/p = 0
.. p = 3
A price of $3 per unit will yield a maximum profit.
q(10) = k/10^3 = 64
k = 64,000
Revenue = q(p)*p = 64000/p^2
Cost = 150 +2q = 150 +2*64000/p^3
Profit = Revenue -Cost = 64000/p^2(1 -2/p) -150
Differentiating to find the maximum profit, we have
.. dProfit/dp = -2(64000/p^3) +6(64000/p^4) = 0
.. -1 +3/p = 0
.. p = 3
A price of $3 per unit will yield a maximum profit.