Question

For the given cost function ,C(x)=3136+787x+x^2

a) The average cost at the production level 49 is

b) The marginal cost at the production level 49 is

c) The production level that will minimize the average cost is

Answer 1

Step 1)

we have,

Hence we can say that average cost is given by,

Hence we can say that average cost at the production level of 49 is given by,

Hence we can say that average cost at production level 49 is 900

Step 2)

we have,

Hence we can say that marginal cost is given by,

Hence we can say that marginal cost at the production level of 49 is given by,

Hence we can say that marginal cost at production level 49 is 885

Step 3)

we have,

we have,

Hence we can say that average cost is given by,

we can write,

equate it to 0 we can say that,

quantity demanded(production level) cannot be negative hence,

we can say that x = 56 is the critical point of average cost function

we have,

Hence,

Hence,

Hence we can say that average cost is minimum at a production level of 56 units