SOLUTION: For a certain company, the cost function for producing x items is C(x)=50x+200 and the revenue function for selling x items is R(x)=−0.5(x−120)2+7,200. The maximum capacity of

Algebra ->  Functions -> SOLUTION: For a certain company, the cost function for producing x items is C(x)=50x+200 and the revenue function for selling x items is R(x)=−0.5(x−120)2+7,200. The maximum capacity of       Log On


   

Question 1178251: For a certain company, the cost function for producing x items is C(x)=50x+200 and the revenue function for selling x items is R(x)=−0.5(x−120)2+7,200. The maximum capacity of the company is 140 items.
Assuming that the company sells all that it produces, what is the profit function?
P(x)=
Preview Change entry mode .
Hint: Profit = Revenue - Cost as we examined in Discussion 3.
What is the domain of P(x)?
Hint: Does calculating P(x) make sense when x=−10 or x=1,000?
The company can choose to produce either 70 or 80 items. What is their profit for each case, and which level of production should they choose?
Profit when producing 70 items =
Number

Profit when producing 80 items =
Number

Can you explain, from our model, why the company makes less profit when producing 10 more units?
Found 2 solutions by ikleyn, MathLover1:
Answer by ikleyn(52750) About Me  (Show Source):
You can put this solution on YOUR website!
.

See this TWIN problem solved under this link

https://www.algebra.com/algebra/homework/Finance/Finance.faq.question.1167022.html



Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

For a certain company, the cost function for producing x+items is
C%28x%29=50x%2B200+
and the revenue function for selling x items is
R%28x%29=-0.5%28x-120%29%5E2%2B7200
The maximum capacity of the company is 140 items.
Assuming that the company sells all that it produces, what is the profit function?
P%28x%29=R%28x%29-+C%28x%29
P%28x%29=-0.5%28x-120%29%5E2%2B7200-%2850x%2B200+%29

What is the domain of P%28x%29?
Note that the company can sell at least+0 items and at most 140+items. Thus, the domain is
0%3C=x%3C=140
The company can choose to produce either 70 or 80 items. What is their profit for each case, and which level of production should they choose?
Profit when producing 70 items =
so, if x=70
P%28x%29=-0.5%2870-120%29%5E2%2B7200-%2850%2A70%2B200+%29
P%28x%29=5950+-+3700
P%28x%29=2250

Profit when producing 80 items =
if x=80
P%28x%29=-0.5%2880-120%29%5E2%2B7200-%2850%2A80%2B200+%29
P%28x%29=6400+-+4200
P%28x%29=2200
Can you explain, from our model, why the company makes less profit when producing 10 more units?
there is max number of units where square function (parabola) goes up, after that goes down
the maximum is when x=-b%2F2a
P%28x%29=-0.5%28x-120%29%5E2%2B7200-%2850x%2B200+%29-expand
P%28x%29+=+-0.5x%5E2+%2B+70+x+-+200
The maximum is: x=-b%2F2a=-70%2F%282%2A-0.5%29=-70%2F-1=70 or 70+ units
=> for 80 units the cost is higher and profit lower