The demand quantity Q of a commodity is the function of price P, q = 1 / 5 (28-p), and the total cost function C = q ^ 2 + 4q. Find: how many units of products are produced, and the profit is the largest What is the maximum profit?

Profit q = Q * P-C;
Find Q to maximize Q, q = 1 / 5 (28-p), that is, P = 28-5q;
Q=q（28-5q）-（q^2+4q）=-6q^2+24q； It can be seen that q = 2 has a maximum value, q = 24

Suppose that the total cost function of an enterprise producing a commodity is C (q) = 1 / 4q ^ 2 + 8q + 4900 (yuan), and the demand is q = 1 / 3 (528-p) (ton), where p is the price Ask (1) how many tons are produced each month to maximize the profit? What is the maximum profit? (2) When the profit reaches the maximum, what is the price P of the commodity?

Write out the profit function to find the maximum

Suppose that the demand function and supply function of a complete market are d = 22-4p and S = 4 + 2p respectively. Find (1) the equilibrium price and equilibrium quantity of the market. (2) single completion Suppose that the demand function and supply function of a complete market are d = 22-4p and S = 4 + 2p respectively. Find (1) the equilibrium price and quantity of the market. (2) the demand function of a single perfectly competitive manufacturer

1,d=s p=3 d=s=10
2. The demand function of perfectly competitive manufacturers is a horizontal line, P = 3
Because in a perfectly competitive market, the manufacturer does not affect the market price, and its supply curve is p = MC, so when MC = Mr = P, it is the manufacturer's output Q

Function definition? Constituent elements? (detailed answers)

Function is a kind of correspondence in mathematics, which is the correspondence from nonempty number set a to real number set B. simply speaking, a changes with B, and a is the function of B. to be precise, let X be a nonempty set, y be a nonempty number set, and f be a corresponding rule. If there is a unique element Y in Y corresponding to each x in X according to the corresponding rule F, it is said that the corresponding rule f is a function on X, Note that y = f (x), X is the definition field of function f (x), set {y | y = f (x), X ∈ r} is its value field (the value field is a subset of Y), X is called independent variable, y is called dependent variable, and it is customary to say that y is a function of X
Correspondence rule and definition domain are two elements of function

What are the two elements of a function?

Definition domain and corresponding rules

What are the three elements of a function? Among the three elements (), the two functions are different functions The two functions of () in the three elements are the same function

Domain definition
range
Correspondence rule
(as long as there is one different)
(domain, correspondence rule)

The demand quantity Q of a commodity is the function of price P, q = 1 / 5 (28-p), and the total cost function C = q ^ 2 + 4q. Find: how many units of products are produced, and the profit is the largest What is the maximum profit?