Suppose we have the demand function given as p=72−7,5q, where q is the number of units to be produced and sold. Determine the marginal revenue after 3 units have been sold
Question
Suppose we have the demand function given as p=72−7,5q, where q is the number of units to be produced and sold. Determine the marginal revenue after 3 units have been sold
Solution
The marginal revenue is the derivative of the total revenue with respect to quantity.
First, we need to find the total revenue function. The total revenue (TR) is the price (p) times the quantity (q). So, we substitute p from the demand function into the total revenue function:
TR = p*q = (72 - 7.5q) * q = 72q - 7.5q^2
Next, we find the derivative of the total revenue function with respect to q to get the marginal revenue (MR):
MR = d(TR)/dq = d(72q - 7.5q^2)/dq = 72 - 15q
Finally, we substitute q = 3 into the marginal revenue function to find the marginal revenue after 3 units have been sold:
MR = 72 - 15*3 = 72 - 45 = 27
So, the marginal revenue after 3 units have been sold is 27.
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