The demand function for a product is p=30−3q where p is the price in dollars when q units are demanded. find the level of production that maximizes the total revenue and determine the revenue. a) q= units
b) r= $

A) Quantity, q = 5 units.

B) Revenue, r = $75.

Step-by-step explanation:

The demand function for a product is

where p is the price in dollars when q units are demanded.

Revenue = Price × Quantity

Using the given information, the revenue function is

         .... (1)

Differentiate with respect to q.

Equate to find the critical value of q.

Divide both sides by q.

The value of q is 5.

Differentiate with respect to q.

So, the revenue function is maximum at q=5.

Substitute q=5 in equation (1).

Therefore, the level of production that maximizes the total revenue is 5 units and the revenue is $75.

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step-by-step explanation: