# Detailed Optimization Calculations

Please help with the following problem.

Optimization:

Giant Screen TV, Inc, is a manufacturer and distributor of high-resolution 50-inch television monitors and consoles for individual and commercial customers. Revenue and cost relations are:

TR = $4,500Q - 0.1Q^2

MR = $4,500 - 0.2Q

TC = $2,000,000 + $1,500Q + 0.5Q^2

MC = $1,500 + $Q

A. Calculate output, marginal cost, average cost, price, and profit at the average cost-minimizing activity level.

B. Calculate these values at the profit-maximizing activity level.

C. Compare and discuss your answers to part A and B.

https://brainmass.com/economics/output-and-costs/detailed-optimization-calculations-454076

#### Solution Preview

a) Calculate output, marginal cost, average cost, price, and profit at the average cost-minimizing activity level.

At the cost-minimization point, MC = ATC

ATC = TC/Q = 2000000/Q + 1500 + 0.5Q

Let MC = ATC

1500 + Q = 2000000/Q + 1500 + 0.5Q

0.5Q = 2000000/Q

0.5Q^2 = 2000000

Q^2 = ...

#### Solution Summary

Given a firm's cost and revenue functions, this solution shows the precise, detailed mathematical calculations necessary to maximize a firm's revenues and minimize its costs.