Example 1: You decide to set up a small business making home-
made chocolate boxes. Your startup costs are Rs. 1600 and you incur
additional Rs. 40 per box. By selling your chocolate boxes, you
found out that the amount of revenue you get is given by the
function: where the number of boxes of
chocolate you sell. How many boxes of chocolate do you have to sell
to break even?
Solution:
, Example 2: A plastic chair manufacturer decides to set up a small production
plant for manufacturing chair. The fixed cost per year is Rs. 20 lakhs. The
additional cost (Variable Cost) for producing each school chair is Rs. 400. Each
chair is sold at Rs. 800. During the first year 6000 chairs are produced and sold:
(i) Determine the cost function C(X) for the total cost of producing X chairs.
(ii) Determine the Revenue Function R(X) for the total revenue from the sale of
X chairs.
(iii) Determine the profit function P(X) for the profit from the sale of X chairs.
(iv) What profit or loss the company incurs during the first year when all the
6000 chairs are sold?
(v) Determine the break-even point.
Solution: (i) C(X) = 400 x +2000000, (ii) R(X) = 800 x, (iii) P(x) =
400 x -2000000, (iv) Rs. 400000 profit, (v) x = 5000
made chocolate boxes. Your startup costs are Rs. 1600 and you incur
additional Rs. 40 per box. By selling your chocolate boxes, you
found out that the amount of revenue you get is given by the
function: where the number of boxes of
chocolate you sell. How many boxes of chocolate do you have to sell
to break even?
Solution:
, Example 2: A plastic chair manufacturer decides to set up a small production
plant for manufacturing chair. The fixed cost per year is Rs. 20 lakhs. The
additional cost (Variable Cost) for producing each school chair is Rs. 400. Each
chair is sold at Rs. 800. During the first year 6000 chairs are produced and sold:
(i) Determine the cost function C(X) for the total cost of producing X chairs.
(ii) Determine the Revenue Function R(X) for the total revenue from the sale of
X chairs.
(iii) Determine the profit function P(X) for the profit from the sale of X chairs.
(iv) What profit or loss the company incurs during the first year when all the
6000 chairs are sold?
(v) Determine the break-even point.
Solution: (i) C(X) = 400 x +2000000, (ii) R(X) = 800 x, (iii) P(x) =
400 x -2000000, (iv) Rs. 400000 profit, (v) x = 5000
