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Let the profit function of an enterprise be l (q) = 10 + 2q-0.1q ², What is the output Q for maximum profit?
L（q）=10+2q-0.1q ²=- 0.1（q ²- 20q-100）=-0.1（q-10） ²+ twenty
From the above formula, when (Q-10) = 0, l (q) is the largest, that is, when the profit is the largest, the output is 10 and the profit is 20
Let the demand function of a commodity be q = 100-5p, where Q and P represent the demand quantity and price respectively. If the demand elasticity of a commodity is Eq EP greater than 1 (where EQ EP＝−Q′ QP, q 'is the derivative of Q), then the value range of commodity price P is __
∵ q = 100-5p, elastic EQ
EP greater than 1
∴EQ
EP＝−Q′
QP=5P
100−5P＞1
∴（P-10）（P-20）＜0
∴10＜P＜20
So the answer is: (10, 20)
Let the functional relationship between the price P of a commodity and the demand Q be p = 24-2q
Total sales = price * sales volume = P * q, because P = 24-2q, q = (24-p) / 2, so p * q = P * (24-p) / 2
The demand quantity Q of a commodity is a function of price P, q = 150-2p ^ 2, when p = 6, if the price decreases by 2%, the total income changes by 100%
The total return is s = P * q = P * (150-2p ^ 2) = 150p-2p ^ 3. The total return change is DS = (150-6p ^ 2) * DP. The total return change rate is DS / S = (150-2p ^ 2) / (150-6p ^ 2) * (DP / P). When p = 6, the price decreases by 2%, that is, DP / P = - 2%, the total return change rate is DS / S = (150-2 * 6 ^ 2) / (150-6 * 6 ^ 2) * (- 2%) = 78 /
Suppose the demand quantity Q of a commodity is a function of price P, q = 5-2p ^ 0.5, then at the level of P = 4, if the price decreases by 1%, the demand quantity will increase________ RT. solve ah. Speed ha!
Q = 5-2p ^ 0.5 when p = 4, q = 1
dQ/dP=P^(-0.5)
dQ=P^(-0.5)dP
When DP = 4 * (- 1%) = -0.04
P=4
dQ=1/2*(-0.04)=-0.02
Therefore, the demand will be reduced by 0.02 to 2%
The commodity price is 5 yuan, the demand is 1500 yuan, the price is 10 yuan, and the demand is 1000 yuan. Please refer to the demand function for details
Let y = ax + B, then 5A + B = 1500, 10a + B = 1000, the solution is a = - 100, B = 2000, then the analytical formula of the function is y = 2000-100x
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