Acompany plans to sell pens for $2 each. the company’s financial planner estimates that the cost, y, of manufacturing the pens is a quadratic function with a y-intercept of 120 and a vertex of (250, 370). what is the minimum number of pens the company must sell to make a profit?

Option B is correct

The minimum number of pens the company must sell to make a profit is, 174.

Explanation:

Let x be the number of pens  and y be the cost of the pens.

To find the cost of the equation.

It is given that cost , y , of manufacturing the pens is a quadratic function i.,e

                [1]

and  y-intercept of 120 which means that for x=0 , y=120 and Vertex = (250 , 370).

Put x = 0  and y =120  in [1]

120 = 0+0+c

⇒  c= 120.

Since, a quadratic function has axis of symmetry.

The axis of symmetry is given by:

                [2]

Substitute the value of x = 250 in [2];

or

                        [3]

Substitute the value of x=250, y =370, c =120 and b = -500 a in [1];

 or

or

or

1 = -250 a

⇒

We put the value of a in [3]

So,

b =-500 a=

Simplify:

b =2

Therefore, the cost  price of the pens is:  

And the selling  of the pens is 2x [ as company sell pens $ 2 each]

To find the minimum number of pens the company must sell to make a profit:

profit = selling price - cost price

Since to make minimum profit ; profit =0

then;

or

Simplify:

⇒   or

Simplify:

x =173.205081

or

x = 174 (approx)

Therefore, the minimum number of pens the company must sell to make a profit is, 174

d≈7.07in

step-by-step explanation:

the correct functions are

h(x) = 3x + 2  

g(x) = 2^x

step-by-step explanation:

i proceed to calculate the different values ​​of k (x)

case 1)  k(x) = g(x) ∘ h(x)

g(x) ∘ h(x)=g(h(x))

k(x) = [2]^[3x + > is the option  4. k(x) = 2^(3x + 2 )

case 2)  k(x) = g(x) + h(x)

k(x) = [2^x]+[3x + 2]=2^x+3x+> is the option  1.) k(x) = 2^x + 3x + 2

case 3)k(x) = h(x) ÷ g(x)

k(x) =  [3x + 2]/[2^x]=3x/(2^x)+2/(2^x)=3x*(2^-x)+2^(1-x)

is the option  3.)   k(x) = (3x)2^(-x) + 2^(-x + 1 )

case 4)k(x) = g(x) - h(x)

k(x) =  [2^x]-[3x + 2]=2^x-3x-> is the option  2.) k(x) = 2^x - 3x - 2 

case 5)  k(x) = g(x) × h(x)

k(x) = [2^x]*[3x + > is the option  5.) k(x) = 2^x(3x + 2)

case 6)k(x) = h(x) ∘ g(x)

h(x) ∘ g(x)=h(g(x))

k(x)=3*[2^x]+> is the option  6. k(x) = 3(2^x) +2