Can someone please help me with this?? im trying to correct answers and i need help

Could you help me to solve the problem below the cost for producing x items is 50x+300 and the revenue for selling x items is 90

s344n2d4d5 [400]

Answer:

Profit function: P(x) = -0.5x^2 + 40x - 300

profit of $50: x = 10 and x = 70

NOT possible to make a profit of $2,500, because maximum profit is $500

Step-by-step explanation:

(Assuming the correct revenue function is 90x−0.5x^2)

The cost function is given by:

$C(x) = 50x + 300$

And the revenue function is given by:

$R(x) = 90x - 0.5x^2$

The profit function is given by the revenue minus the cost, so we have:

$P(x) = R(x) - C(x)$

$P(x) = 90x - 0.5x^2 - 50x - 300$

$P(x) = -0.5x^2 + 40x - 300$

To find the points where the profit is $50, we use P(x) = 50 and then find the values of x:

$50 = -0.5x^2 + 40x - 300$

$-0.5x^2 + 40x - 350 = 0$

$x^2 - 80x + 700 = 0$

Using Bhaskara's formula, we have:

$\Delta = b^2 - 4ac = (-80)^2 - 4*700 = 3600$

$x_1 = (-b + \sqrt{\Delta})/2a = (80 + 60)/2 = 70$

$x_2 = (-b - \sqrt{\Delta})/2a = (80 - 60)/2 = 10$

So the values of x that give a profit of $50 are x = 10 and x = 70

To find if it's possible to make a profit of $2,500, we need to find the maximum profit, that is, the maximum of the function P(x).

The maximum value of P(x) is in the vertex. The x-coordinate of the vertex is given by:

$x_v = -b/2a = 80/2 = 40$

Using this value of x, we can find the maximum profit:

$P(40) = -0.5(40)^2 + 40*40 - 300 = $500$

The maximum profit is $500, so it is NOT possible to make a profit of $2,500.

3 0

3 years ago

The probability that your call to a service line is answered in less than 30 seconds is 0.85. Assume that your calls are indepen

aev [14]

Answer:

a) 0.1720

b) 0.8298

c) 19

Step-by-step explanation:

For each call, there are only two possible outcomes. Either they are answered in less than 30 seconds. Or they are not. The probabilities for each call are independent. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

In this problem we have that:

$p = 0.85$

(a) If you call 12 times, what is the probability that exactly 9 of your calls are answered within 30 seconds? Round your answer to four decimal places (e.g. 98.7654).

This is $P(X = 9)$ when $n = 12$ .

So

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 9) = C_{12,9}.(0.85)^{9}.(0.15)^{3} = 0.1720$

(b) If you call 20 times, what is the probability that at least 16 calls are answered in less than 30 seconds? Round your answer to four decimal places (e.g. 98.7654).

This is $P(X \geq 16)$ when $n = 20$