Given the demand function q = 6750-50p, the total cost function TC = 12000 + 0.025q2 (Q2 is the quadratic power of Q), the maximum profit, output, price and maximum profit can be obtained

Given the demand function q = 6750-50p, the total cost function TC = 12000 + 0.025q2 (Q2 is the quadratic power of Q), the maximum profit, output, price and maximum profit can be obtained

TC=12000+0.025Q^2=12000+0.025*(6750-50P)^2
Profit = pq-tc = P * (6750-50p) - [12000 + 0.025 * (6750-50p) ^ 2]
=6750P-50P^2-12000-6750^2/40+675000P/40-2500P^2/40
=（-4500P^2+945000P+46042500)/40
When the price P = 945000 / (4500 × 2) = 105, the highest profit = 2391375
Output Q = 6750-50 × 105 = 1500

Finding profit function by knowing cost function and supply function

Profit function = supply function - cost function
The supply function s = f (P) indicates that there is a one-to-one correspondence between the supply quantity of a commodity and the price of the commodity. It indicates the relationship between the supply quantity and various factors influencing the supply quantity

The total cost function of a commodity is C = 100 + 3q, the demand function is q = - 100p + 1000, where p is the unit price of the commodity, and the maximum profit of the commodity is obtained

From q = - 100p + 1000, P = 10-0.01q
π=TR-TC=PQ-TC=（10-0.01Q）Q-（100+3Q）=-0.01Q2+7Q-100
π‘=-0.02Q+7=0
Q=350
Maximum profit π = - 0.01 * 350 square + 7 * 350-100 = 1125

The maximum profit problem of quadratic function
When the purchase price of each car is 290000 yuan, an average of 8 cars can be sold every week. When the sales price is reduced by 5000 yuan, an average of 4 more cars can be sold every week. If each car is reduced by X Yuan, the sales profit of each car is y yuan
1: Find the functional relationship between Y and X. write the value range of X under the condition of ensuring that the business does not lose money
2: Suppose the average weekly sales profit of this kind of car is z0000 yuan
3: When the price of each car is tens of thousands of yuan, the average weekly sales profit is the largest? What is the maximum profit
Don't answer if you want to be clear. I want to understand this question
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Nanbo Auto City sells a certain type of car, and the purchase price of each car is 250000 yuan. Market research shows that when the sales price is 290000 yuan, an average of 8 cars can be sold every week, and when the sales price is reduced by 5000 yuan, an average of 4 more cars can be sold every week. If the price of each car is reduced by X 10000 yuan, the sales profit of each car is y 10000 yuan. (sales profit = sales price purchase price)
(1) Find the functional relationship between Y and X, and write out the value range of X on the premise that the business does not lose money;
(2) Suppose that the average weekly sales profit of this kind of car is z0000 yuan, try to write the functional relationship between Z and X;
(3) When the price of each car is 10000 yuan, the average weekly sales profit is the largest? What is the maximum profit?
Analysis: we know the equivalent relationship "sales profit = sales price - purchase price", from which we can get the functional relationship between Y and X, Z and X
（1） y=-x+4
（2） z=-8xx+24x+32
(3) When the price is 275000 yuan, the maximum profit is 500000 yuan
When the price is 275000 yuan, the maximum profit is 500000 yuan