The management of Lorimar Watch Company has determined that the daily marginal revenue function associated with producing and selling their travel clocks is given by

R '(x) = -0.003x + 12
where x denotes the number of units produced and sold and R '(x) is measured in dollars/unit.
(a) Determine the revenue function R(x) associated with producing and selling these clocks.
R(x) =

(b) What is the demand equation that relates the wholesale unit price p with the quantity of travel clocks demanded?
p =

To determine the revenue function R(x), we need to find the antiderivative of the marginal revenue function R'(x).

Taking the antiderivative of -0.003x + 12 with respect to x gives us:

R(x) = ∫(-0.003x + 12) dx

Integrating -0.003x gives us:

R(x) = -0.003 * (x^2/2) + 12x + C

Where C is the constant of integration. Since we are determining the revenue function, we are interested in finding the exact value of R(x), so we can ignore the constant of integration.

Thus, the revenue function R(x) associated with producing and selling these clocks is:

R(x) = -0.003 * (x^2/2) + 12x

Now, to determine the demand equation that relates the wholesale unit price p with the quantity of travel clocks demanded, we can rearrange the revenue function:

R(x) = p * x

Substituting the revenue function -0.003 * (x^2/2) + 12x for R(x):

-0.003 * (x^2/2) + 12x = p * x

Simplifying the equation, we get:

-0.003 * (x^2/2) + (12 - p) * x = 0

This is the demand equation that relates the wholesale unit price p with the quantity of travel clocks demanded.