Question

Brach and Larue is a home goods store chain, and it is about to introduce a new convection oven that’s expected to sell very well across its stores. These are the projected revenue and cost functions for the ovens:
R(x) = -13.85x2 + 1,660x
C(x) = 55,400 – 279x

What is the maximum profit that can be made from selling the ovens?

Answer 1

Answer:

$\ 12,465$

Step-by-step explanation:

The functions for cost and revenue are given below:

$Projected \:Revenue,R(x)= -13.85x^2 + 1660x\\ Projected Cost, C(x)=55400 -279x\\Projected Profit = Revenue-Cost=R(x)-C(x)\\=-13.85x^2 + 1660x-(55400 -279x)\\=-13.85x^2 + 1660x-55400 +279x\\P(x)=-13.85x^2 + 1939x-55400$

The profit will be maximized at its line of symmetry,$x=-\dfrac{b}{2a}$

From P(x), a=-13.85, b=1939

Line of symmetry,

$x=-\dfrac{b}{2a}=-\dfrac{1939}{2(-13.85)}=70$

The maximum profit that can be made will occur when x=70

$P(x)=-13.85x^2 + 1939x-55400\\P(70)=-13.85(70)^2 + 1939(70)-55400\\=\ 12,465$

The maximum profit that can be made form the sales of the oven is $12,465.