(i)
Given TFC of product=35000, TVC=500x, where x=no. of units of product, required cost function=C(x)=35000+500x.
Given R(x)=5000x−100x2.
Thus P(x)=R(x)−C(x)=5000x−100x2−35000−500x,
P(x)=4500x−100x2−35000
(ii)
For breakeven point, P(x)=0 ⇒ 4500x−100x2−35000=0 ⇒ x=10,x=35.
(iii)
For loss, P(x)<0 ⇒ x2−45x+350>0 ⇒ x>35 or x<10.
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