Answer:
[tex]\$12,465[/tex]
Step-by-step explanation:
The functions for cost and revenue are given below:
[tex]Projected \:Revenue,R(x)= -13.85x^2 + 1660x\\$Projected Cost, C(x)=55400 -279x\\Projected Profit = Revenue-Cost=R(x)-C(x)\\=-13.85x^2 + 1660x-(55400 -279x)\\=-13.85x^2 + 1660x-55400 +279x\\P(x)=-13.85x^2 + 1939x-55400[/tex]
The profit will be maximized at its line of symmetry,[tex]x=-\dfrac{b}{2a}[/tex]
From P(x), a=-13.85, b=1939
Line of symmetry,
[tex]x=-\dfrac{b}{2a}=-\dfrac{1939}{2(-13.85)}=70[/tex]
The maximum profit that can be made will occur when x=70
[tex]P(x)=-13.85x^2 + 1939x-55400\\P(70)=-13.85(70)^2 + 1939(70)-55400\\=\$12,465[/tex]
The maximum profit that can be made form the sales of the oven is $12,465.
