# Optimal output level by marginal cost minimization

A firm has determined that its variable costs are given by the following relationship:

VC = .05Q3 - 5Q2 + 500Q

where Q is the quantity of output produced.

Determine the output level where marginal costs are minimized.

333.3

33.3

3.33

© BrainMass Inc. brainmass.com October 9, 2019, 6:06 pm ad1c9bdddfhttps://brainmass.com/economics/pricing-output-decisions/optimal-output-level-marginal-cost-minimization-78549

#### Solution Preview

VC = .05Q3 - 5Q2 + 500Q , marginal cost is the incremental change in variable cost

Marginal cost function is obtained by ...

#### Solution Summary

First order derivative approach used to derive optimal quantity by minimizing marginal cost function

$2.19