The supply equation for an olive oil press is
S(q) = 5q^2 + 1,000q + 100
where S(q) is the price in dollars at which q units are supplied. Find the quantity supplied in a month when the company sets the price of its olive oil press at $12,820

Respuesta :

Answer:

12 units

Step-by-step explanation:

The given function is

[tex]S(q) = 5q^2 + 1000q + 100[/tex]

where, S(q) is the price in dollars at which q units are supplied.

We need to find the quantity supplied in a month when the company sets the price of its olive oil press at $12,820.

Substitute S(q)=12820 in the given function.

[tex]12820 = 5q^2 + 1000q + 100[/tex]

Subtract both sides by 12820.

[tex]0= 5q^2 + 1000q - 12720[/tex]

Taking out GCF.

[tex]0= 5(q^2 + 200q - 2544)[/tex]

Now solve the equation for q by splitting the middle term.

[tex]0= 5(q^2 + 212q-12q - 2544)[/tex]

[tex]0= 5(q(q + 212)-12(q + 212))[/tex]

[tex]0= 5(q + 212)(q-12)[/tex]

Using zero product property we get

[tex]q + 212=0\Rightarrow q=-212[/tex]

[tex]q-12=0\Rightarrow q=12[/tex]

q is number of units. So the value of q can not be negative.

Therefore the quantity supplied in a month when the company sets the price of its olive oil press at $12,820 is 12 units.