Question

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

Answer 1

12 units

Explanation:

The given function is

`S(q) = 5q^2 + 1000q + 100`

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.

`12820 = 5q^2 + 1000q + 100`

Subtract both sides by 12820.

`0= 5q^2 + 1000q - 12720`

Taking out GCF.

`0= 5(q^2 + 200q - 2544)`

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

`0= 5(q^2 + 212q-12q - 2544)`

`0= 5(q(q + 212)-12(q + 212))`

`0= 5(q + 212)(q-12)`

Using zero product property we get

`q + 212=0\Rightarrow q=-212`

`q-12=0\Rightarrow q=12`

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.