Given the cost function, C(x), and the revenue function, R(x), find the number of units x that must be sold to break even

1 answer:

8 0

P(x) = R(x) - C(x) Breaking even is the point where revenue starts to overtake cost. It is, therefore, the point where P(x) = 0. Since these are all linear functions, you know that after that point the business is profitable. P(x) = 0R(x) - C(x) = 015000x - (9000x+72000) = 015000x - 9000x - 72000 = 06000x - 72000 = 06000x = 72000x = 72000/6000x = 12 At 12 units the business breaks even.

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Answer:

(a) 0.4242

(b) 0.0707

Step-by-step explanation:

The total number of ways of selecting 8 herbs from 12 is

$\binom{12}{8}=495$

(a) If 2 herbs are selected, then there are 8 - 2 = 6 herbs to be selected from 12 - 8 = 10. The number of ways of the selection is then

$\binom{10}{6}= 210$

Note that this is the number of ways that both are included. We would have multiplied by 2! if any of them were to be included.

The probability = $\dfrac{210}{495}=0.4242$

(b) If 5 herbs are selected, then there are 8 - 5 = 3 herbs to be selected from 12 - 5 = 7. The number of ways of the selection is then

$\binom{7}{3}= 35$

This is the number of ways that both are included. We would have multiplied by 5! if any of them were to be included. In that case, our probability will exceed 1; this implies that certainly, at least, one of them is included.

The probability = $\dfrac{35}{495}=0.0707$