A manufacturer produces and sells pens Rs 10 per unit. His fixed costs

1.	A manufacturer produces and sells pens Rs 10 per unit. His fixed costs are Rs 600 and variable cost per pen is Rs 3.50. Calculate (i) Revenue function (ii) Cost function (iii) Profit function (iv) Break even point.
Answer» (i) Revenue function R(x) = p.x. = lQx (ii) Cost function C(x) = ax + b (iii) Profit function p(x) = Rx – C(x) = 8x – [3.50x + 6500] (iv) Break even point at BEP ⇒ TR = TC ⇒ R(x) = R(x) ⇒ P(x) = 0 ∴ 4.50x – 6500 = 0 ⇒ x = 6500/4.500 = 1445. units Break even point revenue is RS = 1445 × 10 = Rs. 14450

A manufacturer produces and sells pens Rs 10 per unit. His fixed costs are Rs 600 and variable cost per pen is Rs 3.50. Calculate (i) Revenue function (ii) Cost function (iii) Profit function (iv) Break even point.

Answer»

(i) Revenue function R(x) = p.x. = lQx

(ii) Cost function C(x) = ax + b

(iii) Profit function p(x) = Rx – C(x) = 8x – [3.50x + 6500]

(iv) Break even point at BEP ⇒ TR = TC ⇒ R(x) = R(x) ⇒ P(x) = 0

∴ 4.50x – 6500 = 0 ⇒ x = 6500/4.500 = 1445. units

Break even point revenue is RS = 1445 × 10 = Rs. 14450