The cost C (in dollars) for the care and maintenance of a horse and carriage is C=15x+2000 where x is the number of rides.

Mathematics

1 answer:

MissTica3 years ago

6 0

Answer: 100 rides are needed to break even.

Step-by-step explanation:

We have given the cost function

C(x)=15x+2000 where x is the number of rides.

And rides cost 35$

⇒ revenue function would be 35 times x

i.e.R(x)=35 x , where x is the number of rides.

Break even point of a firm occurs when at a certain point x the total cost equals to the total revenue.

i.e. at break even point

total revenue=total cost

⇒35x=15x+2000

⇒35-15x=2000[subtract 15x from both sides]

⇒20x=2000 [simplify]

⇒x=2000/20[dividing both sides with 20]

⇒x=100

∴ 100 rides are needed to break even.

You might be interested in

<img src="https://tex.z-dn.net/?f=81-%28y-1%29%28y%5E2%2B27%29%20%5Cgeq%200%20%5C%5C%5C%5C%2081-%28y%5E3%2B27y-y%5E2-27%29%20%5C

Zarrin [17]

First thing you'll need to know is that the value for this equation is actually an approximation 'and' it is imaginary, so, one method is via brute force method.

You let f(y) equals to that equation, then, find the values for f(y) using values from y=-5 to 5, you just substitute the values in you'll get -393,-296,-225,... till when y=3 is f(y)=-9; y=4 is f(y)=48, so there is a change in signs when 'y' went from y=3 to y=4, the answer is between 3 and 4, you can work out a little bit deeper using 3.1, 3.2... You get the point. The value is close to 3.1818...

The other method is using Newton's method, it is similar to this but with a twist because it involves differentiation, so $y_{n+1}=y_n-\frac{f(y)}{f'(y)}$ where 'n' is the number you approximate, like n=0,1,2... etc. f(y) would the equation, and f'(y) is the derivative of f(y), now what you'll need to do is substitute the 'n' values into 'y' to find the approximation.