Information to solve problems
Q=12L+29L^2-1.1L^3
Q= # of cars produced/year
L=# of laborers used per year for production
Each car sells for $125.
$7000 per laborer per year is cost for labor and other consumable materials.
I attempted some parts of these questions and some parts I did not understand. Can someone check my work and help me with the parts I didn't get?
Questions:
1. What is the max and min number of laborers possible for the production of cars? This is the domain of what function?
I answered this one this way.
12L+29L^2-1.1L^3=0
L(12+29L-1.1L^2)=0
L=0, 26.77, -0.41
The minimum number of laborers would be 0.
The maximum number of laborers would be 26.77.
I don't know the answer to: this is the domain of what function?????
2. How many laborers would be needed to maximize the production of cars?
Q'=12+58L-3.3L^2
12+58L-3.3L^2=0
L=17.78, -0.20
Q'(max)=17.78
To maximize the production they need 17.78 laborers.
3. How many laborers would be needed to maximize the revenue for producing cars? What is the maximum revenue?
Revenue = price * production
=$125 * 26.8 = 3350 laborers ( I'm not sure if this is right)
Revenue (max)= price * Q'(max)
$125 * ((12*17.78) +(29*(17.78^2))-(1.1*(17.78^3))
Revenue(max)=$399,780.54
4. Is there a range of values of production for the cars that would be profitable? IF so, what is the range?
Profit = price*production-7000L
L(-137.5L^2+3625L-5500)=0
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?