Answer:
12 units
Step-by-step explanation:
The given function is
![S(q) = 5q^2 + 1000q + 100](https://tex.z-dn.net/?f=S%28q%29%20%3D%205q%5E2%20%2B%201000q%20%2B%20100)
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](https://tex.z-dn.net/?f=12820%20%3D%205q%5E2%20%2B%201000q%20%2B%20100)
Subtract both sides by 12820.
![0= 5q^2 + 1000q - 12720](https://tex.z-dn.net/?f=0%3D%205q%5E2%20%2B%201000q%20-%2012720)
Taking out GCF.
![0= 5(q^2 + 200q - 2544)](https://tex.z-dn.net/?f=0%3D%205%28q%5E2%20%2B%20200q%20-%202544%29)
Now solve the equation for q by splitting the middle term.
![0= 5(q^2 + 212q-12q - 2544)](https://tex.z-dn.net/?f=0%3D%205%28q%5E2%20%2B%20212q-12q%20-%202544%29)
![0= 5(q(q + 212)-12(q + 212))](https://tex.z-dn.net/?f=0%3D%205%28q%28q%20%2B%20212%29-12%28q%20%2B%20212%29%29)
![0= 5(q + 212)(q-12)](https://tex.z-dn.net/?f=0%3D%205%28q%20%2B%20212%29%28q-12%29)
Using zero product property we get
![q + 212=0\Rightarrow q=-212](https://tex.z-dn.net/?f=q%20%2B%20212%3D0%5CRightarrow%20q%3D-212)
![q-12=0\Rightarrow q=12](https://tex.z-dn.net/?f=q-12%3D0%5CRightarrow%20q%3D12)
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.
Answer:
A= 335.5 units squared
Step-by-step explanation:
Why not write all of the numbers in decimal fraction form, to make them easier to compare?
68 2/3 = 68.666...
72 1/2 = 72.500
68 3/10 = 68.300
74 7/11 = 74.636...
68 1/2 = 68.500
550/8 = 68.750
Now ask yourself: Which of the last four numbers is between 68.666.. and 72.500?