Answer to Question #350145 in Calculus for Vickie

Question #350145

The fixed cost of a company is 35000 and the variable cost per unit is 500 and the revenue function for sale is X units is given by R(x)=5000X-100X2

I) find the profit function

Ii) break even values

III)the values of X which results in a loss


1
Expert's answer
2022-06-16T15:02:41-0400

(i)

Given TFC of product=35000\text{TFC of product} = 35\,000, TVC=500x\text{TVC} = 500x, where x=no. of units of productx=\text{no. of units of product}, required cost function=C(x)=35000+500x\text{required cost function} = C(x)=35\,000+500x.

Given R(x)=5000x100x2R(x)=5\,000x-100x^2.

Thus P(x)=R(x)C(x)=5000x100x235000500xP(x)=R(x)-C(x)=5\,000x-100x^2-35\,000-500x,

P(x)=4500x100x235000P(x)=4\,500x-100x^2-35\,000

(ii)

For breakeven point, P(x)=0P(x)=0 \Rightarrow 4500x100x235000=04\,500x-100x^2-35\,000=0 \Rightarrow x=10,x=35x=10, x=35.


(iii)

For loss, P(x)<0P(x)<0 \Rightarrow x245x+350>0x^2-45x+350>0 \Rightarrow x>35x>35 or x<10x<10.


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