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# Detailed Optimization Calculations

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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.

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.

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