Question

If the marginal cost (MC) of production of the company is directly proportional to the number of units (x) produced, then find the total cost function, when the fixed cost is ₹ 5,000 and the cost of producing 50 units is ₹ 5,625

Answer 1

M.C αx

M.C = λx

fixed cost k = ₹ 5000

Cost function C = `int ("M.C")  "d"x`

= `int lambdax  "d"x`

C = `(lambdax^2)/2 + "k"`

⇒ C = `lambda (x^2/2) + 5000`  ........(1)

When x = 50 then C = 5625

5625 = `(lambda(50)^2)/2 + 5000`

5625 – 5000 = `(lambda(2500))/2 = 1250 lambda`

`1250 lambda = 625`

⇒ `lambda = 625/1250 = 1/2`

∴ Required total cost function from equation (1)

C = `1/2(x^2/2) + 5000`

∴ C = `x^2/4 + 5000`