# demand function

There are two different problems of calculus (see the attachment).

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#### Solution Preview

Please find solutions/explanations attached herewith.

1) Consider the demand function for selling x widgets given by

p(x) = 30(ln(40)+1) -30ln(x)

a) Find the revenue generated by selling x widgets.

Revenue R(x) = xp(x)

R(x) = x*(30(ln(40)+1) -30ln(x))

R(x) = 30x(ln(40)+1) -30xln(x)

b) Assume that the production level is related to the number of employees by the formula x =10n where n is the number of employees. Find the revenue generated as a function of n employees.

Put x = 10n

R(n) = 30*(10n) (ln(40)+1) -30*10n*ln(10n)

R(n)= 300n(ln(40)+1) - 300nln(10n)

R(n)= 300n(ln(40)+1) -300n(ln(10)+ln(n))

R(n)= 300nln(40) + 300n - 300n(1n(10) + ln(n))

R(n)= 300nln(40) + 300n - 300nln(10) - 300nln(n)

R(n)= 300nln(40) - 300nln(10) + 300n - 300nln(n)

R(n)= ...

#### Solution Summary

Find the revenue generated in this case.