Given the cost function C(x) = 43 x + 4576 and the revenue function R(x) = 65 x, find the break-even point and the profit function.

The break-even point in format (a,b) is:
profit function p(x)=

break-even is where cost = revenue.

43x+4576 = 65x
...
P(x) = R(x)-C(x)

To find the break-even point, we need to set the cost function equal to the revenue function and solve for x.

Setting the cost function C(x) equal to the revenue function R(x), we have:

43x + 4576 = 65x

To isolate x, we can subtract 43x from both sides:

4576 = 22x

Dividing both sides by 22:

x = 4576/22

Simplifying the fraction:

x = 208

So the break-even point is x = 208.

To find the profit function, we need to subtract the cost function from the revenue function. The profit function p(x) is given by:

p(x) = R(x) - C(x)

Substituting the given revenue and cost functions:

p(x) = 65x - (43x + 4576)

Simplifying:

p(x) = 65x - 43x - 4576

Combining like terms:

p(x) = 22x - 4576

So, the profit function is p(x) = 22x - 4576.