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stellarik [79]
3 years ago
12

For a​ monopolist's product, the demand function is p equals 75 minus 0.05 q and the cost function is c equals 700 plus 25 q​, w

here q is number of​ units, and both p and c are expressed in dollars per unit. At what level of output will profit be​ maximized? At what price does this​ occur, and what is the​ profit?
Mathematics
1 answer:
Sergio039 [100]3 years ago
6 0

Answer:

The correct answer is at 500 units offering at $50, the monopolist will have a profit equal to $11,800.

Step-by-step explanation:

For a​ monopolist's product, where q is number of​ units, and both p and c are expressed in dollars per unit,

Demand function is p = 75 - 0.05 × q

Revenue function is R = Demand function × Quantity = 75 × q - 0.05 × q^{2}

Cost function is c = 700 + 25 × q​

Profit function is given by π = R - c = 75 × q - 0.05 × q^{2} - 700 - 25 × q​

⇒ π = -0.05 ×q^{2} + 50 × q - 700

Now for profit to be​ maximum ⇒ \frac{d}{dq}π = 0

⇒ -0.1 ×q + 50 = 0

⇒ 0.1 × q = 50

⇒ q = 500.

We can easily see that the second order derivative is negative hence telling us that the profit is maximum.

There at 500 units of the product the monopolist will have his maximum output.

Price at which the profit occurs = 75 - 0.05 × 500 = $50

Profit = -0.05 × 500 × 500 + 50 × 500 - 700 = -12500 + 25000 -700 = $11800

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Olegator [25]

Answer:

Reject <em>H</em>₀. There is a significant difference in drug resistance between the two states.

Step-by-step explanation:

In this case we need to determine whether the data suggest a statistically significant difference between the proportions of drug-resistant cases in the two states.

The significance level of the test is, <em>α</em> = 0.02.

(1)

The hypothesis can be defined as follows:  

<em>H</em>₀: There is no difference between the proportions of drug-resistant cases in the two states, i.e. p_{1} - p_{2}=  0.  

<em>Hₐ</em>: There is a statistically significant difference between the proportions of drug-resistant cases in the two states, i.e. p_{1} - p_{2}\neq  0.  

(2)

Compute the sample proportions and total proportion as follows:

\hat p_{1}=\frac{12}{189}=0.063\\\\\hat p_{2}=\frac{8}{429}=0.019\\\\\hat p=\frac{12+8}{189+429}=0.032\\

Compute the test statistic value as follows:

Z=\frac{\hat p_{1}-\hat p_{2}}{\sqrt{\hat p(1-\hat p)\times [\frac{1}{n_{1}}+\frac{1}{n_{2}}]}}

   =\frac{0.063-0.019}{\sqrt{0.032(1-0.032)\times [\frac{1}{189}+\frac{1}{429}]}}\\\\=2.86

The test statistic value is 2.86.

(3)

The decision rule is:

The null hypothesis will be rejected if the p-value of the test is less than the significance level.

Compute the p-value as follows:

p-value=2\cdot P(Z>2.86)=2\times 0.00212=0.00424

<em>p</em>-value = 0.00424 < <em>α</em> = 0.02.

The null hypothesis will be rejected at 0.02 significance level.

Reject <em>H</em>₀. There is a significant difference in drug resistance between the two states.

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3 years ago
Hii! If someone could plz help me!
sergeinik [125]

Answer:

-4.5 is less than 3

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-3/2 = -1.5

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Is it possible to have more than one (x,y)(x,y) pair that is a solution to both equations? Explain or show your reasoning
lesya692 [45]

Answer with step-by-step explanation:

Yes, it is possible to have more that one (x,y) pair because of the distributive property.

6x + 4y = 34. If this is the case, we have to find 2 numbers that sum up to 34.

  • x = 3
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5x - 27 = 15. If we are going to calculate this equation, you need to reverse the equation. 15 + 27 = 42 = 5x. If 42 = 5x, we have to divide 42 by 5, which is 8.4

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Step-by-step explanation:

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Equation 2 is y=x+8 when n=1 (arbitrary choice). Note that m is not equal to n.

A typical example of the required system is Eqn 1: y=-3x+4 and Eqn 2: y=x+8.
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