Posted by Janet on Thursday, April 21, 2011 at 11:15pm.
The domain of a function f(x) is the range of values of x which is admitted by the function f.
For example, the domain of
is (-∞,+∞), or all real numbers.
On the other hand, the domain of
f(x)=ln(x) is (0,∞), since the function ln(x) cannot accept non-positive values of x.
In this case, since we cannot hire a negative person, so the domain starts at ______ and goes up to _______.
The domain applies to the function _______=12L+29L^2-1.1L^3.
For the maximum production, you will need to find dQ/dL and equate it to zero to find the maximum (or minimum).
3. Revenue R(L) is the selling price minus the cost.
Selling price = $125*Q(L)
cost = $7000L
Again, find L for maximum R(L) by equating dR/dL=0.
4. Profitable means R(L)>0.
Find the interval on which R(L)>0, i.e. find the lower and upper limits of L between which R(L)>0.
Note that L must be an integer.
1. So this is the answer I got 12L+29L^2-1.1L^3=0
L=0, 26.77, -0.41
The minimum number of laborers would be 0.
The maximum number of laborers would be 26.77.
THe range would then be (0,26.77) because when I substitute a number >26.77 into the above equation it becomes a negative number. Am I on the right track or still way off?
To maximize the production they need 17.78 laborers
3. TO figure out how many laborers would be needed to maximize the revenue for producing cars?
How would I set that up?
4.Profit = price*production-7000L
L=0, 1.56, 24.9
The range would be 1.56 - 24.9. (I'm not sure if this is right).
How would I justify this answer with a graph? SHow the graphs of the 1st and 2nd derivatives?
1)Q=0 if L=-0.41 or L=0 or L=26.77
Q>=0 if 0<=L<=26
2)Q'=12+58L-3.3L^2=0 if L=17.78
Q(17)=3180.7 and Q(18)=3196.8, therefore L=18
3)The revenue R=(12L+29L^2-1.1L^3)x125-7000L
R'=-5500+7250L-412.5L^2=0 if L=16.75
R(16)=276800 and R(17)=278587.5,
4)R=0 if L=0 or L=1.6 or L=24.7
R>=0 if 2<=L<=24
Carry on with the problem.. To find maximum profit, not revenue, would I take the derivative of the profit function, which I have as
Profit=125*(12L+29L^2-1.1^3)-7000L. If I take the derivative of this(which I'm not sure I did right) my L=16.78 or .79. If I plug it back into the original profit function my max comes out to 278746.76. Does this look right?
Calculus - Information to solve problems Q=12L+29L^2-1.1L^3 Q= # of cars ...
Math Modeling - How is the number of cars and other vehicles changing over time...
math - a factory increases the production of cars annually by 8% if presently it...
social studies - i really need some help on finding information on the Barbados...
English Language - I asked this question earlier. I need to write 2 letters of ...
introductory algebra - I had these problems on my test and for some reason got ...
Math help needed .??? - I really need help in answering the steps and the answer...
Microeconomics - Check and correct my answers please. Thank you. Trunks owns a ...
AlgebraII - I really stuck on binomial theorem and I have a whole worksheet due ...
please i need help accounting - i have a promblem it gives me the information ...
For Further Reading