50 POINTS

Suppose the cost function associated with a product is C(x)= cx+F dollars and the revenue function is R(x) where C denotes the unit cost of production, S the unit selling price, F the fixed cost incurred by the firm, and X the level of production and sales.

Find the break-even quantity and the break-even revenue in terms of the constants C,S, and F

please explain

The break-even quantity is the level of production and sales at which the total cost equals the total revenue. We can find the break-even quantity by setting the cost function equal to the revenue function and solving for x.

The cost function is given by C(x) = cx + F, and the revenue function is R(x) = Sx.

Setting the cost and revenue functions equal gives us:

cx + F = Sx

To find the break-even quantity, we solve for x:

cx - Sx = -F

x(c - S) = F

x = F / (c - S)

So, the break-even quantity in terms of the constants C, S, and F is x = F / (c - S).

To find the break-even revenue, we can substitute the break-even quantity back into the revenue function:

R(x) = Sx

R(F / (c - S)) = S * (F / (c - S))

So, the break-even revenue in terms of the constants C, S, and F is R(F / (c - S)) = S * (F / (c - S)).