I have a question about two problems that I am trying to solve for my h.s. trig. class. The first one I believe is correct. the other i am lost.
D(p)= 2000-60p
S(p)=460+94p p is the price in dollars
a) find those values of p for which demand exceeds supply
2000-60P > 460 + 94p
2460 > 154p
$15.97 > p
b) find those value of p for which demand is less than supply
2000-60P < 460 + 94p
2460 < 154p
p > $15.97
Second problem
The yearly Egyptian production of oil O(t) in millions of barrels, t years after 2000 can be approximated by,
O(t)=-40.4t +2159
Using inequality, determine the years for which the production will drop below 1750 million barrels.
This is what I have and know I have set it up wrong.
o(t)=-40.5t + 2159
O(t)>1750
-40.5t>1750-2159
-40.5t> -409/-40.5
I do not feel good about completing this...think I have it wrong
For the first problem, you correctly set up the inequality for part (a) and solved it correctly. The answer p > $15.97 means that for prices greater than $15.97, the demand will exceed the supply.
For part (b), you set up the inequality incorrectly. The correct equation is:
2000 - 60P < 460 + 94P
Simplifying it further:
154P > 1540
P > 10
This means that for prices greater than $10, the demand will be less than the supply.
For the second problem, you made a small mistake:
O(t) = -40.4t + 2159
To find the years for which the production drops below 1750 million barrels, you need to set up the inequality correctly:
-40.4t + 2159 < 1750
Now, solve it:
-40.4t < 1750 - 2159
-40.4t < -409
Dividing both sides by -40.4, remember to flip the inequality sign since we are dividing by a negative number:
t > -409 / -40.4
t > 10.13
This means that the production will drop below 1750 million barrels for years greater than 10.13 years after 2000.