Question

Suppose you are the manager of a firm. The accounting department has provided cost​ estimates, and the sales department sales​ estimates, on a new product. Analyze the data they give​ you, determine what it will take to break​ even, and decide whether to go ahead with production of the new product. The product has a production cost function ​C(x)equals75xplus3 comma 350 and a revenue function ​R(x)equals100x.

Answer 1

Answer:

If more than 134 articles are produced and sold, the firm will have positive profits and shoule start production

Step-by-step explanation:

Cost, Revenue, and Profit Function

The cost function C(x) is given by

$C(x)=75x+3,350$

where x is the number of produced products.

The revenue function is

$R(x)=100x$

With both equations, we can know the profit function as

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

$P(x)=100x-75x-3,350=25x-3,350$

$P(x)=25x-3,350$

For the firm to have positive profits, it has to produce x articles with the condition

$P(x)>0$

Or, equivalently

$P(x)=25x-3,350>0$

Solving for x

$\displaystyle x>\frac{3,350}{25}$

Thus

$x>134$

This means that if more than 134 articles are produced and sold, the firm will have positive profits and shoule start production