The inverse demand function for soybeans is p = 30,000

Question

The inverse demand function for soybeans is p = 30,000 - 6q.Total revenue in this market will be maximized when the quantity of soybeans produced is
A)3,611 bushels.
B)5,000 bushels.
C)1,250 bushels.
D)2,500 bushels.
E)none of the above.

Quizplus · Accepted Answer

To maximize revenue, we need to find the quantity at which marginal revenue equals zero. 
The inverse demand function is given by:
p = 30000 - 6q 
Total revenue (TR) is given by the product of price (p) and quantity (q): 
TR = pq = (30000 - 6q)q

Taking the derivative of TR with respect to q:

d(TR)/dq = 30000 - 12q

Setting this equal to zero:

30000 - 12q = 0

Solving for q:

q = 2500

Therefore, the quantity of soybeans produced that will maximize revenue is 2,500 bushels.