Solution:
Given:
[tex]Revenue\text{ function, R\lparen x\rparen= -x}^2+134x[/tex]
To find the selling price, x, which will give highest revenue, y, we will find maximum value of parabola curve −x² + 134x
The value of -b/2a tells us the value x of the vertex of the function
−x² + 134x
a = -1
b = 134
Thus,
[tex]\begin{gathered} x=-\frac{b}{2a}=\frac{-134}{2(-1)}\text{ = }\frac{-134}{-2}\text{ = 67} \\ x=67 \end{gathered}[/tex]
The selling price which will give highest revenue= 67 dollars per backpack
R = −x² + 134x
When x = 67
R = −67² + 134(67)
R= -4489 + 8978
R= 4489
Thus, the maximum revenue is 4489 dollars
Summary:
67 dollars per backpack goes into the first box
4489 dollars goes into the second box
