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brilliants [131]
3 years ago
10

Suppose you are the manager of a firm. The accounting department has provided cost​ estimates, and the sales department sales​ e

stimates, 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.
Mathematics
1 answer:
Katarina [22]3 years ago
6 0

Answer:

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

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

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==================================================

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