Question

The price-demand and cost functions for the production of microwaves are given as

p = 275 − x 60
p = 275 - x 60
and
C(x) = 50000 + 30x

where x is the number of microwaves that can be sold at a price of p dollars per unit and C(x) is the total cost (in dollars) of producing x

Required:
a. Find the profit function in terms of x.
b. Find the marginal cost as a function of x.
c. Find the revenue function in terms of x.
d. Find the marginal revenue function in terms of x.

Answer 1

Answer:

ALTERNATIVE 1

a. Find the profit function in terms of x.

P(x) = R(x) - C(x)

P(x) = (-60x² + 275x) - (50000 + 30x)

P(x) = -60x² + 245x - 50000

b. Find the marginal cost as a function of x.

C(x) = 50000 + 30x

C'(x) = 0 + 30 = 30

c. Find the revenue function in terms of x.

R(x) = x · p

R(x) = x · (275 - 60x)

R(x) = -60x² + 275x

d. Find the marginal revenue function in terms of x.

R'(x) = (-60 · 2x) + 275

R'(x) = -120x + 275

The answers do not make a lot of sense, specially the profit and marginal revenue functions. I believe that the question was not copied correctly and the price function should be p = 275 - x/60

ALTERNATIVE 2

a. Find the profit function in terms of x.

P(x) = R(x) - C(x)

P(x) = (-x²/60 + 275x) - (50000 + 30x)

P(x) = -x²/60 + 245x - 50000

b. Find the marginal cost as a function of x.

C(x) = 50000 + 30x

C'(x) = 0 + 30 = 30

c. Find the revenue function in terms of x.

R(x) = x · p

R(x) = x · (275 - x/60)

R(x) = -x²/60 + 275x

d. Find the marginal revenue function in terms of x.

R(x) = -x²/60 + 275x

R'(x) = -x/30 + 275