Q=200-2P so that Marginal Revenue is MR=100-Q.

To find the marginal revenue (MR) and profit-maximizing quantity, we need to differentiate the total revenue function with respect to P and equate it to the marginal revenue.

Given:
Total Revenue (TR) = Q * P
MR = 100 - Q

We can substitute the value of TR into the formula for MR to get:
100 - Q = d(TR)/dP

To find d(TR)/dP, we differentiate the total revenue function (TR = Q * P) with respect to P.

d(TR)/dP = (d(Q)/dP) * P + Q * (d(P)/dP)
= Q + P * (d(Q)/dP)

Since Q = 200 - 2P, we substitute this back into the equation:
d(TR)/dP = (200 - 2P) + P * (d(200 - 2P)/dP)
= (200 - 2P) + P * (-2)
= 200 - 2P - 2P
= 200 - 4P

Now, equate the derivative to the marginal revenue:
100 - Q = 200 - 4P

Next, solve for Q in terms of P:
Q = 200 - 4P - 100
Q = 100 - 4P

To find the profit-maximizing quantity, set MR equal to the marginal cost (MC) and solve for Q:
100 - Q = MC

Without the information on the marginal cost, we cannot find the profit-maximizing quantity or determine other properties of the function.