1. It is known that when q products are produced, the daily total cost function C(q)=80+ 10q, and the demand function q(p)=p+6(p is the price). How many products will be produced every day when the factory breaks even (that is, breakeven point)? What is the average cost when breaking even?

Solution:

When the factory breaks even, the marginal cost MC=dC/dq= 10=p=q-6.

Output q * =16;

Average cost AC = c/q = 80/16+10 =15.

2. The total cost of a factory producing q tons of products per month is: C=80+2q (unit: yuan), and the total income from selling these products per month is: r = 30q-q 2 (unit: yuan). What is the profit and average profit of selling 10 products?

Solution: Profit π(q)=R-C=-q2+28q-80, and profit π (10) =100 from selling10 products.

The average profit is π (10)10 =10.