Question

Suppose that the cost C of obtaining water that contains p percent impurities is given by

C(p) = 

140,000

p

 − 1400.

(a) Find 

lim p→100⁻ C(p),

 if it exists. (If you need to use  or –, enter INFINITY or –INFINITY, respectively.)

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Answer 1

SOLUTION :

a.

C(p) = 140000 / p - 1400 

lim p -> 100 -  C(p)

= lim p -> 100 - (140000/p - 1400)

= 140000/100 - 1400

= 0 

Interpret the result : 

Option : This is basically untreated water. (ANSWER).

b.

C(p) = 140000 / p - 1400 

lim p -> 0+  C(p)

= lim p -> 0+ (140000/p - 1400)

= (140000/0+)  - 1400

= + INFINITY  (undefined extremely large value)

c,

Is complete purity possible?

OPTION : No, because the cost would be extremely large since, C(0) is undefined. (ANSWER)