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.

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elcharly64 elcharly64 · Answer 1 · 2020-02-18T15:15:40+01:00

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

[tex]C(x)=75x+3,350[/tex]

where x is the number of produced products.

The revenue function is

[tex]R(x)=100x[/tex]

With both equations, we can know the profit function as

[tex]P(x)=R(x)-C(x)[/tex]

[tex]P(x)=100x-75x-3,350=25x-3,350[/tex]

[tex]P(x)=25x-3,350[/tex]

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

[tex]P(x)>0[/tex]

Or, equivalently

[tex]P(x)=25x-3,350>0[/tex]

Solving for x

[tex]\displaystyle x>\frac{3,350}{25}[/tex]

Thus

[tex]x>134[/tex]

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