Question

A company sells widgets. The amount of profit, y, made by the company, is related to the selling price of each widget, x, by the given equation. Using this equation, find out the maximum amount of profit the company can make, to the nearest dollar. y=-35x^2+1458x-8400

Answer 1

67.84

Explanation:

y=-35x^2+1458x-8400

y=−35x

2

+1458x−8400

\text{Find: Max Profit}\rightarrow\text{y-value}

Find: Max Profit→y-value

x

y

(21, 6784)

y=$67.84{Max profit}

y=$67.84→Max profit

Answer 2

$6,786.09

Explanation:

Calculation to find out the maximum amount of profit the company can make, to the nearest dollar

Based on the information given we would have to find the value of y since x is the line of symmetry by using this formula

x=-b/(2a)

Where,

a = -35

b = 1458

Let plug in the formula

x=-1458/(2)(-35)

x=-1458/-70

x=1,458/70

Now let put the value of x above into this formula y=-35x^2+1458x-8400 in order for us to find the value of y

y=-35x^2+1458x-8400

y=(-35)(1458/70)^2+1458(1458/70)-8400

y=(-35)(433.83)+1,458(20.83)-8400

y=-15,184.05+30,370.14-8400

y=$6,786.09

Therefore the maximum amount of profit the company can make, to the nearest dollar is $6,786.09