Question #53342

A study indicated that the average cost function for a high school is

AC=10.3-0.4Q+0.00012Q^2, where Q is the number of students in the school.

a) What size school (i.e in terms of number of students) results in minimum average cost?

b) Find equations for total and marginal cost.

AC=10.3-0.4Q+0.00012Q^2, where Q is the number of students in the school.

a) What size school (i.e in terms of number of students) results in minimum average cost?

b) Find equations for total and marginal cost.

Expert's answer

AC=10.3-0.4Q+0.00012Q^2,

a) Such size of school (i.e in terms of number of students) results in minimum average cost, for which AC' = 0, so:

-0.4 + 0.00024Q = 0

Q = 0.4/0.00024 = 1667 students.

b) The equations for total and marginal cost can be found in such way:

TC = AC*Q = 10.3Q - 0.4Q^2 + 0.00012Q^3

MC = TC' = 10.3 - 0.8Q + 0.00036Q^2

a) Such size of school (i.e in terms of number of students) results in minimum average cost, for which AC' = 0, so:

-0.4 + 0.00024Q = 0

Q = 0.4/0.00024 = 1667 students.

b) The equations for total and marginal cost can be found in such way:

TC = AC*Q = 10.3Q - 0.4Q^2 + 0.00012Q^3

MC = TC' = 10.3 - 0.8Q + 0.00036Q^2

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