The monthly profit from the sale of a product is given by P = 18x − 0.1x2 − 100 dollars.
(a) What level of production maximizes profit?
(b) What is the maximum possible profit?
Solution :-
Given data :
The monthly profit from the sale of a product is given by P = 18x − 0.1x2 − 100 dollars.
(a) What level of production maximizes profit?
Here consider differentiation of P with respect to x, we get
Again consider differentiation with respect to x, we get
< 0
Here,P will be maximum at critical point. i.e
18 - 0.2 x =0
18 = 0.2 x
x = 90
Therefore, level of production maximizes profit ,x = 90.
(b) What is the maximum possible profit?
The maximum possible profit,
The monthly profit from the sale of a product is given by P = 18x −...
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