Question

For a monopolisks product, the demand function is p=75−0.05q and the cost function is c=300+25q, where q is number of units, and both p and c are axpressed in dolars per una At what ierei of output will profit be maximized? At what prico does this ocour, and what is the profiT? The profit will be makimized at an output of ___units. (Simplify your angwer. Type an integar of a decimal.)

Answer 1

The profit-maximizing output is 8 units, and the price at this output is 74.6 dollars per unit. The resulting profit is 596.8 dollars.

Step-by-step explanation:

To maximize profit, we need to find the output level (q) at which marginal revenue (MR) equals marginal cost (MC). In this case, MR = MC is represented by the demand function and cost function.

So, we can set 75-0.05q = 300+25q.

Solving this equation, we find q = 8.

To find the price at which this occurs, we can substitute the value of q into the demand function.

So, p = 75-0.05(8) = 75-0.4 = 74.6 dollars per unit.

The profit can be calculated by multiplying the profit-maximizing quantity (8 units) by the profit-maximizing price (74.6 dollars per unit).

So, the profit is 8 * 74.6 = 596.8 dollars.