Suppose that the demand curve faced by a monopoly manufacturer is p = 10 – 3q and the cost function is TC = q ^ 2 + 2q, find the output, price and profit when the manufacturer's profit is maximum?

Suppose that the demand curve faced by a monopoly manufacturer is p = 10 – 3q and the cost function is TC = q ^ 2 + 2q, find the output, price and profit when the manufacturer's profit is maximum?

From the meaning of the question:
MR=10-6Q
MC=2Q+2
When the profit is very large, Mr = MC
Obtained: q = 1
P=10-3Q=7
Profit r = pq-tc = 8q-4q2 = 4

It is known that the functional relationship between the production cost C and the output Q of a commodity is C = 100 + 4q, and the functional relationship between the price P and the output Q is p = 25 - [(1 / 8) q] The answer is this: profit z = pq-c The production cost here is gross, not multiplied by Q? Isn't the cost possible?

The production cost is only related to output, not price. The products are rotten in the warehouse, and the cost will not be less
Profit z = pq-c = [25 - (1 / 8) q] q-100-4q = - (1 / 8) Q ^ 2 + 21q-100,
DZ / DQ = - Q / 4 + 21 = 0, when q = 84, the profit is the largest

It is known that the functional relationship between the production cost C and the output Q of a commodity is C = 100 + 4q, and the functional relationship between the unit price P and the output Q is p = 25-1 / 8q. What is the value of Q and the maximum profit l Detailed process

Revenue r = q · P = q (25-q) = 25q-q2, profit L = R-C = (25q-q2) - (100 + 4q) = - Q2 + 21q-100 (0 ＜ Q ≤ 200), l '= - Q + 21, let L' = 0, i.e. - Q + 21 = 0, the solution is q = 84. Because when 0 ＜ Q ＜ 84, l '> 0; When 84 ＜ Q ＜ 200, l ′＜ 0, so when q = 84, l gets the maximum value. A: when the output is 84, l takes

It is known that the functional relationship between the cost C of a commodity and the output Q is C = 100 + 4q, and the functional relationship between the unit price P and the output Q is p = 25-0.25q What is the maximum profit l when the output Q is

L=pq-C=25q-0.25q^2-100-4q=-0.25q^2+21q-100
It can be seen from the above formula that L-Q is a parabola with the opening downward, so the extreme point is the highest point, i.e. l max
On the derivative of Q over L, l '= -0.5q + 21
Let L '= 0, then q = 42
So max L = -0.25 × 42^2+21 × 42-100=341
A: when the output Q is 42, the profit L is the largest and 341

If the cost function of a commodity is C (q) = the square of Q - 4q + 12, and Q is the output, what is the fixed cost?

Fixed cost means that even if you don't produce a cost
That is, the value of C when q = 0
When q = 0, C = 12, so 12 is a fixed cost

Know that the functional relationship between commodity cost C and output Q is C = 1000 + 4q, and the functional relationship between unit price P and output Q is q = 25 - (1 / 8) Q. when finding the value of Q, each piece Know that the functional relationship between commodity cost C and output Q is C = 1000 + 4q, and the functional relationship between unit price P and output Q is q = 25 - (1 / 8) Q. when finding the value of Q, the average profit l of each product is the largest

The functional relationship between unit price P and output Q is q = 25 - (1 / 8) Q
Is the relationship wrong?
Profit = sales - cost
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