Answer:
The maximum profit will be: $605.125
Step-by-step explanation:
Given the function
[tex]y\:=\:-2x^2\:+\:105x\:-\:773[/tex]
The given equation is a quadratic function. It represents Parabola. The parabola opens down because of the negative leading coefficient (-2).
Thus, the maximum profit would be computed at the vertex of the graph.
Thus, we have to determine the value of y when x is the line of symmetry.
We can find this by the equation
x = -b/2a
where a = -2, b = 105
x = -105 / 2(-2)
x = -105 / -4
x = 105/4
x = 26.25
Now, putting x = 26.25 in the original function to find the value of 'y'.
[tex]y\:=\:-2x^2\:+\:105x\:-\:773[/tex]
[tex]y=-2\left(26.25\right)^2+105\left(26.25\right)-773[/tex]
[tex]y=-2\cdot \:26.25^2+105\cdot \:26.25-773[/tex]
[tex]y=1983.25-1378.125[/tex]
[tex]y=605.125[/tex]
Therefore, the maximum profit will be: $605.125
